Are there non-medical miracles that can get a person beatified/canonized?

St. Rita of Cascia: Saint of the Impossible: Wife, Mother, Widow, Nun (1381-1457) by Joseph Sicardo, O.S.A., ch. 30:

On the 27th of April, in the year 1652, a house belonging to Signora Clara Calderini, wife of Giovanni Polidoro, a resident of Narni, took fire accidentally. Owing to the scarcity of water, all hope of saving the building was abandoned. The fire, however, was extinguished almost immediately by throwing into the flames a small piece of woollen cloth which had touched the veil of St. Rita. This fact is attested by the officials of the city of Narni, May 21st of the same year.

From the Decree of St. Rita's Canonization (ibid. ch. 36):

The first miracle consists of that pleasing scent emanating from the remains of the Saint’s body, the existence of which is confirmed by many reliable witnesses and trustworthy tradition, so that to doubt concerning this fact would be absurd; moreover no natural cause can be given for the existence of this odor, as we see from the physical research which has been made by men most skilled in such things. Furthermore this odor diffuses itself in a manner above the usual laws of nature. Hence we should be persuaded that this fragrance has its origin through divine intervention.

Yes.

Miracles for beatification or canonisation do not have to be medical. The Congregation for the Causes of Saints, the Vatican investigative body, only retain, on a general basis, medical experts, but can consult other technical expertise, as well as medical specialists, when needed. Another stage in the process of validating a miracle is considering whether it is something God might reasonably be expected to have done, which is pretty much a given in the case of healings.

In the last hundred years miracles have included visions, delivery from accidents (by means of a broken rope, and of a flash of light) and a miracle of multiplication (similar in principle to the Multiplication of the Loaves and Fishes.

The rest of this answer reports some instances.

Miracle of Multiplication - occurred in 1949

St. John Macias was born in Western Spain in 1585. He emigrated to South America, eventually settling in Lima, Peru. He became a lay brother at the Dominican Priory of St. Mary Magdalene in that city, where he worked as doorkeeper until his death in 1645. He was known to levitate. He provided food for many of the poor people in Lima. Donations were collected for him by a donkey who, following certain regular routes through the more prosperous districts, brayed loudly to inform residents he was there to receive donations in his pack. Many miracles were recorded during his life, and he (John, not the donkey) was beatified in 1837 by Pope Gregory XVI.

In January 1949, in Olivenza, Spain, near where John was born, the following miracle took place. This account is from the New Scientist, 8th April, 1982 (page 74):

On the afternoon of 25 January, 1949, Leandra, the cook of a religious institute in Olivenza, went down to the kitchen to light her stoves. She had to prepare dinner for a group of students who lived in.

It was the invariable habit of the institute to offer dinner to the poor families of the neighbourhood as well, but on this occasion Leandra opened the cupboard to find 3 cups of rice, about 750g [ just over a pound and a half] in all. She proposed to cook this up in water with another 750 grams of meat, some onions and a bay leaf to feed at least the paying students. Then, putting the pot on the fire, Leandra invoked the aid of the Blessed Juan Macias to care for the poor who would find nothing to eat that evening. Then she went on to other tasks, keeping one eye on the fire in the way that any cook does.

After about a quarter of an hour, she stopped to check the rice and was amazed to find it about to spill over the brim of the 10-litre [18 Imperial pints, 21 US pints] kettle. Other cooking pots were produced, one of around 8 litres and another of 10 litres. Leandra and the other women who had swarmed into the kitchen to see what was happening ladled the overflow from the first pot into the second two and, from there, distributed the rice to all comers.

They kept this up for four hours. More than 150 people are reported to have eaten their fill.

It goes on:

The Congregation [for the causes of saints] was able to call 22 eye witnesses.....Most were women from the neighbourhood, not trained observers, but wise in the cooking of rice.

In 1975 when the Congregation concluded its 25-year investigation of these events, the Blessed Juan Macias became Saint John Macias, canonised and promoted mostly on the strength of this miracle.

Miraculous Mountain Rescue through the Snapping of a Rope

Marguerite Bays was born in Siviriez, in the mainly Roman Catholic canton of Fribourg, Switzerland, in 1815. She neither married nor joined a religious order and, as Pope John Paul II said at her Beatification, she was an unaffected woman who lived an ordinary life. She helped her brothers with farm work and also worked locally as a seamstress or dressmaker. She attended Mass almost every day and was active in parish work including catechising children and visiting the sick and old. She suffered from cancer and, rather than pray to be freed of suffering, asked to suffer in a way that would allow her to share more directly in Christ's Passion. On her 39th birthday, 8th September, 1854, she was cured at the exact moment Pope Pius IX proclaimed the Dogma of the Immaculate Conception of Mary. From then on, every Friday she relived, physically and spiritually, the Passion from Gethsemane to Calvary. She suffered with stigmata and wore gloves even in the Summer. She died in 1879.

After her death she was the object of local devotion, but the miracle which led to her beatification, in 2005, took place on Easter Monday, March 25th, 1940.

It is called the Dent-de-Lys Miracle, after the mountain on which it occurred.

Fr. Claude Morel writes of it in pages 16 to 18 of his book "A Closer Acquaintance with the Blessed Marguerite Bays".

The local chaplain took a lady church worker and two male students on an Easter Monday outing to the top of the six thousand foot high mountain, the Dent-de-Lys. They reached the top and began the descent about 4pm. The party were roped together, the idea being that if one slips and falls the others will hold on and so rescue the one who slipped. One of the students,19-year-old Marcel Menetrey, seems to have suffered from vertigo, and was praying to Margeurite to bring them safely down. He went first and reached a ledge, on which he stopped. The others should then have followed one by one, but this seems not to have been followed. The lady slipped and fell and this led to the other two also being jerked into space. Marcel watched his three companions hurtling down past him, expecting when the rope tightened that he too would be pulled down with them. He again called on Marguerite . The rope snapped about ten feet away from him and, although his three companions hurtled to their deaths, he was able to descend the mountain alone and in safety. The breaking of the rope was a miracle, procured by the intervention of Marguerite Bays.

Marcel went on to become a priest, and died in 2000, living to see the Beatification of Marguerite Bays in 1995.

Before Marguerite can become a saint (or, more correctly, be recognised as one) another miracle is needed. One occurred in 1998 when a 22-month-old girl was run over by her grandfather's tractor, but emerged unhurt, following his invocation of Marguerite. This, however, is a medical miracle, as it concerns the health implications of being run over by a tractor. This miracle has been accepted so canonisation is a possibility in the relatively near future. (ADDENDUM - Marguerite was canonised on 13th October 2019.)

This auto-translated article presents a more sceptical view, held by local resident Bernard Pochan who has investigated, and who has said he was abused by a priest aged 15. It also refers, briefly, to theological concerns regarding the limited nature of the miracle.

A Murderer is converted by a vision of his victim

Maria Goretti was born in 1890 in Italy and was a very religious and devoted girl. After her father's death her family shared a house with another family whose mother was dead, , the Serenellis. When she was nearly twelve the Serenelli son, Alessandro, aged 20, wanted to have sex with her but she told him it was against God's will. He threatened to kill her, but she still refused. He then stabbed her several times and went into his room thinking she was dead. When he heard her whimpering he came out and stabbed her some more, fourteen stabs in all.

When their parents (his father and her mother) came back, Maria was taken to hospital and Alessandro to prison. Maria died a day later, saying she forgave Alessandro and wanted him to be with her in heaven.

Maria was credited with many healing miracles but one miracle, mentioned in the case for her beatification, concerned a vision. Alessandro was an angry, unhappy and unrepentant young man. In 1908, about six years after he murdered Maria he had a vision.

The website www.mariagoretti.org says:

But no miracle was to be greater than the conversion of her murderer! It was an astonishing sequel to the drama of a would-be rapist who was sentenced to 30 years of prison. Unrepentent, showing no remorse for his awful crime, Alessandro would undergo a remarkable change. This was to occur after a remarkable dream he had during his 8th year of imprisonment.

The dream was so vivid he could not distinguish it from reality. The prison bars and walls fell away and his cell was a sunlit garden blooming with flowers. Towards him came a beautiful girl dressed in pure white. He said to himself: 'How is this? Peasant girls wear darkish clothes.' But he saw it was Marietta. She was walking among flowers, smiling, and without the least fear. He wanted to flee from her but could not. Marietta picked white lilies and handed them to him saying, 'Alessandro, take them!' He accepted the lilies, one by one, fourteen of them. But a strange thing took place. As he received them from her fingers, the lilies did not remain lilies but changed into so many flaming lights. There was a lily turned to purifying flame for every one of the 14 mortal blows he struck her on the fatal day in Ferriere. Marietta said smilingly, 'Alessandro, as I have promised, your soul shall someday reach me in heaven.'

Contentment entered his breast. And the scene of incredible beauty dissolved in silence. When he awoke, it seemed that the rabid, choking, consuming feelings of hate, destruction, and bitterness that ruled within him were loosening their invisible bonds from his mind and flesh." ("The Penitent" by Pietro DiDonato- Hawthorne Books, N.Y., 1962; pages 109-110)

When he was eventually released he attended mass with Maria's mother who welcomed him as a son, and he ended his days in a monastery.

A Railway Miracle in 1961

A miraculous flash of light, on October 25th, 1961, at Malaga Station in Spain, enabled a man to save his own life. A man called Antony Barres Nararro fell under a train at Malaga Station sand called upon a deceased relative. She was Maria Antonia Bandres Y Elosegui, a Spanish nun who died, aged 21, in 1919. She was well known for her piety and the effect she had on agnostics.

Father John Zuhlzorf describes what happened:

A man behind schedule, rushing to board a moving train, slips off the rain-wet step he jumps at. In front of many witnesses, he falls sidewise between the car and platform onto the track under the wheels of the train. In that instant he has the presence of mind, nay rather the habit and discipline of mind, to call out to Sr. Antonia, a distant relative, to save him. Suddenly a light under the car illuminated a metal tube that the man, large in frame, grabbed hold of with his hands and then hooked with his feet. He was subsequently dragged amidst the train’s wheels in the narrow space between the wheels and the platform. He emerged with torn clothing and some bruises. There was no source of illumination under the car, either artificial or natural. He was dragged over 60 meters in the narrow gap with no serious injury. The experts consulted by the Congregation determined that the light and his escape remained entirely inexplicable by natural causes. The miracle was approved, and Sr. Maria Antonia, who had lived a life of heroic virtue, was beatified on May 12,1996. Her feast is April 27.