Can "feelings and passions" make an act involuntary?

As far as your teacher's statement, it is incorrect. It is entirely possible for a person to

attend Mass on Sunday in the state of grace, commit a mortal sin during the week, and attend Mass the next Sunday having already repented.

Indeed it is possible in theory to commit a mortal sin just after waking up on Sunday morning, experience contrition on the way to Mass, and attend Mass in a state of grace. Mere "feeling remorse", however, won't do the trick. Feeling bad about what you've done, or perhaps fearing that you'll go to hell, or even just that you'll be embarrassed by refraining from Communion - these things aren't enough. The Church calls them "imperfect contrition" or sometimes "attrition". They are morally helpful feelings, but not sufficient to forgive a mortal sin.

Among the penitent's acts contrition occupies first place. Contrition is "sorrow of the soul and detestation for the sin committed, together with the resolution not to sin again."

When it arises from a love by which God is loved above all else, contrition is called "perfect" (contrition of charity). Such contrition remits venial sins; it also obtains forgiveness of mortal sins if it includes the firm resolution to have recourse to sacramental confession as soon as possible.

(Catechism of the Catholic Church, paragraphs 1451–2; emphasis added. The quote is from the Council of Trent.)

As to your main question, though: If one's action arises from "the promptings of feelings and passions", can it thereby become, in effect, involuntary and thus not sinful?

No. The authors of the Catechism were very careful to say that these can "diminish the voluntary... character of the offense", rather than saying that they can remove it.

The Church understands that sometimes one's strong feelings can overcome reason, and cause someone to act in a way they know (rationally) is wrong. Aquinas, for example, says that

sometimes, when the passions are very intense, man loses the use of reason altogether: for many have gone out of their minds through excess of love or anger.

(Summa Theologica, First Part of the Second Part, Question 77, Article 2)

But this loss of reason doesn't necessarily excuse a person entirely. The Catechism does say that responsibility for one's actions "can be diminished or even nullified" (paragraph 1735) by a number of factors. Aquinas agrees, but says that strong conditions apply in order to remove freedom (and thus responsibility) altogether.

Sin consists essentially in an act of the free will, which is a faculty of the will and reason; while passion is a movement of the sensitive appetite.... Accordingly if we take passion as preceding the sinful act, it must needs diminish the sin: because the act is a sin in so far as it is voluntary, and under our control. Now a thing is said to be under our control, through the reason and will: and therefore the more the reason and will do anything of their own accord, and not through the impulse of a passion, the more is it voluntary and under our control. In this respect passion diminishes sin, in so far as it diminishes its voluntariness.

(Summa, First Part of the Second Part, Question 77, Article 6)

In other words, if the strong feeling comes (logically speaking) before the sin, it can impede the use of reason and therefore the ability to act rationally. This diminishes one's responsibility and therefore one's sin.

If, however, the cause [of a person's actions] be not voluntary but natural, for instance, if anyone through sickness or some such cause fall into such a passion as deprives him of the use of reason, his act is rendered wholly involuntary, and he is entirely excused from sin. Sometimes, however, the passion is not such as to take away the use of reason altogether; and then reason can drive the passion away... wherefore such a passion does not excuse from sin altogether.

(Summa, First Part of the Second Part, Question 77, Article 7)

Now in the particular case you mention, there are possible psychological factors that could diminish responsibility. In particular, there seems to be discussion among experts regarding p**nography as an addiction, or as an obsession. Either of these cases could diminish personal responsibility by diminishing the amount of control the rational mind has over the action. (This would not, however, remove the individual's responsibility to care for their mental health so as to become better able to control their actions rationally.)

Now, neither obsession nor addiction describe the case you bring up. In such a case, the person makes an active choice to do something objectively wrong, and serious. This is precisely what is meant by a mortal sin. The fact that this action is consequent to "feelings and passions" makes it more obviously voluntary, not less (as pointed out in another answer).

Is someone strapping you to a chair, propping your eye's open, and forcing you to watch p**nography? If not, then you certainly have freely chosen to watch it and doing so certainly is a mortal sin because:

1. Pornography constitutes grave matter.
   The sex slave / p**nography industry is incredibly inhumane; giving material support to it is itself a sin.
2. You voluntarily watched it.
   Just because you had "feelings and passions" does not mean your act was involuntary. For example, if you become drunk, drive, and kill someone and don't even remember what you did, you are still responsible for having indirectly willed murder.
   ^{For more info on indirectly willed acts, see §94 of Moral Theology by McHugh & Callan, O.P.}
   Also, concupiscence (the body rebelling against the soul, "feelings and passions" inclining you to act against the dictates of reason) does not cause involuntariness, as St. Thomas Aquinas argues in Summa Theologica I-II q. 6 a. 6 co.:

   Concupiscence does not cause involuntariness, but on the contrary makes something to be voluntary. For a thing is said to be voluntary, from the fact that the will is moved to it. Now concupiscence inclines the will to desire the object of concupiscence. Therefore the effect of concupiscence is to make something to be voluntary rather than involuntary.

   ^{Note that CCC 1860 is not claiming that "feelings and passions" make an act involuntary.
   (cf. also St. Thomas's question "Whether ignorance causes involuntariness?".)}
3. You know it's an offense against God:

   St. Matthew 5:28-29:
   …whosoever shall look on a woman to lust after her, hath already committed adultery with her in his heart. And if thy right eye scandalize thee, pluck it out and cast it from thee. For it is expedient for thee that one of thy members should perish, rather than thy whole body be cast into hell.

Lust is a capital sin because other sins (like masturbation in your case) follow from it. Masturbation is an intrinsic evil. Onan "spilled his seed upon the ground" (Gen. 38:9) "And therefore the Lord slew him, because he did a detestable thing" (Gen. 38:10).

The Doctor of the Church St. Thomas Aquinas writes that masturbation is an "unnatural vice" (Summa Theologica II-II q. 154 a. 11 co.)—a type of lust like be*t**lity, sodomy, and pederasty—and that, as in contraception,

procuring pollution [i.e., ejaculation], without any copulation, for the sake of venereal pleasure … pertains to the sin of 'uncleanness' which some call 'effeminacy'*

^{*Latin: mollitiem, lit. 'softness, unmanliness'}

Pray the rosary (at least 5 decades) daily. This is an excellent remedy against sins of impurity.
See

• Part 1, "4^th Decade: Marvellous Effects," of St. Grignion de Montfort's The Secret of the Rosary, which describes how the rosary has converted hardened sinners (including those who prior to praying it were immersed in sins of impurity, like Bl. Alan de la Roche).

• the stories of St. Alphonsus of Liguori's The Glories of Mary.

Marian devotion has a long history of helping those struggling with sins of impurity.