Objection 1. It would seem unlawful to kill men who have sinned. For our Lord in the parable (Matthew 13) forbade the uprooting of the cockle which denotes wicked men according to a gloss. Now whatever is forbidden by God is a sin. Therefore it is a sin to kill a sinner.
Objection 2. Further, human justice is conformed to Divine justice. Now according to Divine justice sinners are kept back for repentance, according to Ezekiel 33:11, "I desire not the death of the wicked, but that the wicked turn from his way and live." Therefore it seems altogether unjust to kill sinners.
Objection 3. Further, it is not lawful, for any good end whatever, to do that which is evil in itself, according to Augustine (Contra Mendac. vii) and the Philosopher (Ethic. ii, 6). Now to kill a man is evil in itself, since we are bound to have charity towards all men, and "we wish our friends to live and to exist," according to Ethic. ix, 4. Therefore it is nowise lawful to kill a man who has sinned.
On the contrary, It is written (Exodus 22:18): "Wizards thou shalt not suffer to live"; and (Psalm 100:8): "In the morning I put to death all the wicked of the land."
I answer that, As stated above (Article 1), it is lawful to kill dumb animals, in so far as they are naturally directed to man's use, as the imperfect is directed to the perfect. Now every part is directed to the whole, as imperfect to perfect, wherefore every part is naturally for the sake of the whole. For this reason we observe that if the health of the whole body demands the excision of a member, through its being decayed or infectious to the other members, it will be both praiseworthy and advantageous to have it cut away. Now every individual person is compared to the whole community, as part to whole. Therefore if a man be dangerous and infectious to the community, on account of some sin, it is praiseworthy and advantageous that he be killed in order to safeguard the common good, since "a little leaven corrupteth the whole lump" (1 Corinthians 5:6).
Reply to Objection 1. Our Lord commanded them to forbear from uprooting the cockle in order to spare the wheat, i.e. the good. This occurs when the wicked cannot be slain without the good being killed with them, either because the wicked lie hidden among the good, or because they have many followers, so that they cannot be killed without danger to the good, as Augustine says (Contra Parmen. iii, 2). Wherefore our Lord teaches that we should rather allow the wicked to live, and that vengeance is to be delayed until the last judgment, rather than that the good be put to death together with the wicked. When, however, the good incur no danger, but rather are protected and saved by the slaying of the wicked, then the latter may be lawfully put to death.
Reply to Objection 2. According to the order of His wisdom, God sometimes slays sinners forthwith in order to deliver the good, whereas sometimes He allows them time to repent, according as He knows what is expedient for His elect. This also does human justice imitate according to its powers; for it puts to death those who are dangerous to others, while it allows time for repentance to those who sin without grievously harming others.
Reply to Objection 3. By sinning man departs from the order of reason, and consequently falls away from the dignity of his manhood, in so far as he is naturally free, and exists for himself, and he falls into the slavish state of the beasts, by being disposed of according as he is useful to others. This is expressed in Psalm 48:21: "Man, when he was in honor, did not understand; he hath been compared to senseless beasts, and made like to them," and Proverbs 11:29: "The fool shall serve the wise." Hence, although it be evil in itself to kill a man so long as he preserve his dignity, yet it may be good to kill a man who has sinned, even as it is to kill a beast. For a bad man is worse than a beast, and is more harmful, as the Philosopher states (Polit. i, 1 and Ethic. vii, 6).
Source: Summa Theologica (New Advent)