Killing a terrorist by official government army consider as bad karma?

Buddhism is all about develop wisdom and wholesome moral and see things as it is. Terrorists are psychopaths suffer from unknown mental decoders due to cling to wrong and unwholesome views. If you respond to them using same methods you don't have difference with them. Just implement and use your wisdom to catch them alive(by firing chemical filled syringes and paralyze) or unconscious(by spreading some gas) and examine and investigate mindset and give proper medicines(defeat their wrong,unethical,immoral and unwholesome ideologies) and counselling(brain wash) using Buddhist teaching for them. killing is not the solution. Don't use lazy and easy way by killing them.Just rehabilitate them as humans. teach them(or brain wash) What is metta,five precept,kindness,eight fold path,four noble truths and Nirvana. That's must be the duty of human worrier in universal army. And this called uncommon wisdom. Don't kill them just cure them.

In the Jataka Tales in the Buddhist Canon, there is the story of the Buddha-To-Be in a past life who killed a would-be murderer to save 500 people, as follows:

And he thought, ‘if I were to kill this person, I would likewise burn in the great hells for one hundred-thousand eons because of it. Yet I can bear to experience the pain of the great hells, that this person not slay these five hundred merchants and develop so much evil karma. I will kill this person myself. Accordingly, the captain Great Compassionate protected those five hundred merchants and protected that person from going to the great hells, by deliberately stabbing and slaying that person who was a robber with a spear, with great compassion and skill in means.

The results of kamma is are known in the heart. If the terrorists are real terrorists then those who act to protect innocent people from terrorists are not really performing bad karma. While a cleanser of terrorists may feel stress & trauma, they can always reassure themselves they did a deed to protect people.

For example, in many civil wars, such as in Sri Lanka, it is difficult to judge if one-side is righteous. But in pure terrorism, it is without dispute that terrorism is evil. In other words, any person killing unarmed civilians is a terrorist. The Dhammapada states:

137. He who inflicts violence on those who are unarmed and offends those who are inoffensive, will soon come upon one of these ten states:

138-140 Sharp pain, or disaster, bodily injury, serious illness, or derangement of mind, trouble from the government, or grave charges, loss of relatives, or loss of wealth, or houses destroyed by ravaging fire; upon dissolution of the body that ignorant man is born in hell.

The Pali suttas state it is the duty of the government to provide protection for the people, as follows:

But what, sire, is this Ariyan duty of a Wheel-turning Monarch?

This, dear son, that thou, leaning on the Norm [the Law of truth and righteousness] honouring, respecting and revering it, doing homage to it, hallowing it, being thyself a Norm-banner, a Norm-signal, having the Norm as thy master, shouldst provide the right watch, ward, and protection for thine own folk, for the army, for the nobles, for vassals, for brahmins, and householders, for town and country dwellers, for the religious world, and for beasts and birds.

DN 26

In Buddhism, monks are forbidden to kill a person or instruct to kill a person, for any reason. But for Buddhist laypeople, taking life is a training rule rather than a commandment. Buddhism does not prohibit people from doing their duty to protect their family & nation. A monk informs people about the potential results of their actions (kamma); that is all.

The Buddha taught kamma is intention. If killing is done from a greedy or hateful intention, this is bad kamma. But if killing is done with compassion for life, this is not bad kamma.

The results of kamma are only known within the heart. The heart knows.

For example, the people in this video are heroes. It can be seen with the heart how their hearts have compassion rather than hatred & violence. These people defeated foreign terrorists & restored their nation to civility & normality (rather than harmed people). After they won, the many people celebrated Xmas & dancing with freedom, as shown in this video.

In the Yodhajiva Sutta, we find that the warrior who has the intention to kill and does exert himself to kill, would be reborn in hell or as an animal:

When a warrior strives & exerts himself in battle, his mind is already seized, debased, & misdirected by the thought: 'May these beings be struck down or slaughtered or annihilated or destroyed. May they not exist.' If others then strike him down & slay him while he is thus striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the hell called the realm of those slain in battle. But if he holds such a view as this: 'When a warrior strives & exerts himself in battle, if others then strike him down & slay him while he is striving & exerting himself in battle, then with the breakup of the body, after death, he is reborn in the company of devas slain in battle,' that is his wrong view. Now, there are two destinations for a person with wrong view, I tell you: either hell or the animal womb."

On the other hand, protection is OK (from DN16):

"What have you heard, Ananda: do the Vajjis duly protect and guard the arahats, so that those who have not come to the realm yet might do so, and those who have already come might live there in peace?"

"I have heard, Lord, that they do."

"So long, Ananda, as this is the case, the growth of the Vajjis is to be expected, not their decline."

In Buddhism, kamma is based on intention. What was the intention of exemplary Buddhist King Asoka? We can see this from The Edicts of King Asoka:

Beloved-of-the-Gods speaks: thus This Dhamma edict was written twenty-six years after my coronation. Happiness in this world and the next is difficult to obtain without much love for the Dhamma, much self-examination, much respect, much fear (of evil), and much enthusiasm. But through my instruction this regard for Dhamma and love of Dhamma has grown day by day, and will continue to grow. And my officers of high, low and middle rank are practicing and conforming to Dhamma, and are capable of inspiring others to do the same. Mahamatras in border areas are doing the same. And these are my instructions: to protect with Dhamma, to make happiness through Dhamma and to guard with Dhamma.

All men are my children. What I desire for my own children, and I desire their welfare and happiness both in this world and the next, that I desire for all men. You do not understand to what extent I desire this, and if some of you do understand, you do not understand the full extent of my desire.

Truly, I consider the welfare of all to be my duty, and the root of this is exertion and the prompt despatch of business. There is no better work than promoting the welfare of all the people and whatever efforts I am making is to repay the debt I owe to all beings to assure their happiness in this life, and attain heaven in the next.

Therefore this Dhamma edict has been written to last long and that my sons, grandsons and great-grandsons might act in conformity with it for the welfare of the world. However, this is difficult to do without great exertion.

One of the five basic Buddhist precept says:

“abstain from harming living beings”

No matter if they are terrorists or monks. Killing is wrong.

I suggest not to worry about what will happen to killers on their next lives, but rather, on the current one. They are getting away from the path of virtue and kindness.

Whole life killing attention is bad kamma, no exception. Even though that bad kamma causes some little good effects. Because killing directly causes bad effect, such as unwholesome mind factors, life's death, etc. Also side effects of killing cause many variant bad effects, too, such as vengeance. Actually, only one killing causes more than ten enemies' vengeance: parents' vengeance, brothers', sisters', aunts', uncles', grandpas', grandmas', partners', sons', daughters', friends', etc.

For the example:

Some americans thought bin laden killing can causes terrorism's cessation. But the fact appearing that we still face the terrorism.

So, buddha said:

Na hi verena verni, sammantīdha kudācanaṃ

Unwholesome (akusalakammapatha, such as vengeance) never ceased by the unwholesome (akusalakammapatha, such as vengeance).

For the last question:

I know some army mens who killed more than 100 terrorists. What will happen for them in next life?

It is answered by Nirayasuttaṃ:

018.03. Bhikkhus, endowed with five things the lay disciple is in hell as though led and lain. What five?

Destroying living things, taking the not given, misbehaving in sexual desires, telling lies and taking intoxicated and brewed drinks Bhikkhus, endowed with these five things the lay disciple is in hell as though led and lain there.

Bhikkhus, endowed with five things the lay disciple is in heaven as though led and lain there. What five?

Abstaining, from destroying living things, taking the not given, misbehaving in sexual desires, telling lies and taking intoxicated and brewed drinks Bhikkhus, endowed with these five things the lay disciple is in heaven as though led and lain there.