Objection 1. It would seem that the judge can lawfully remit the punishment. For it is written (James 2:13): "Judgment without mercy" shall be done "to him that hath not done mercy." Now no man is punished for not doing what he cannot do lawfully. Therefore any judge can lawfully do mercy by remitting the punishment.
Objection 2. Further, human judgment should imitate the Divine judgment. Now God remits the punishment to sinners, because He desires not the death of the sinner, according to Ezekiel 18:23. Therefore a human judge also may lawfully remit the punishment to one who repents.
Objection 3. Further, it is lawful for anyone to do what is profitable to some one and harmful to none. Now the remission of his punishment profits the guilty man and harms nobody. Therefore the judge can lawfully loose a guilty man from his punishment.
On the contrary, It is written (Deuteronomy 13:8-9) concerning anyone who would persuade a man to serve strange gods: "Neither let thy eye spare him to pity and conceal him, but thou shalt presently put him to death": and of the murderer it is written (Deuteronomy 19:12-13): "He shall die. Thou shalt not pity him."
I answer that, As may be gathered from what has been said (A2,3), with regard to the question in point, two things may be observed in connection with a judge. One is that he has to judge between accuser and defendant, while the other is that he pronounces the judicial sentence, in virtue of his power, not as a private individual but as a public person. Accordingly on two counts a judge is hindered from loosing a guilty person from his punishment. First on the part of the accuser, whose right it sometimes is that the guilty party should be punished--for instance on account of some injury committed against the accuser--because it is not in the power of a judge to remit such punishment, since every judge is bound to give each man his right. Secondly, he finds a hindrance on the part of the commonwealth, whose power he exercises, and to whose good it belongs that evil-doers should be punished.
Nevertheless in this respect there is a difference between judges of lower degree and the supreme judge, i.e. the sovereign, to whom the entire public authority is entrusted. For the inferior judge has no power to exempt a guilty man from punishment against the laws imposed on him by his superior. Wherefore Augustine in commenting on John 19:11, "Thou shouldst not have any power against Me," says (Tract. cxvi in Joan.): "The power which God gave Pilate was such that he was under the power of Caesar, so that he was by no means free to acquit the person accused." On the other hand the sovereign who has full authority in the commonwealth, can lawfully remit the punishment to a guilty person, provided the injured party consent to the remission, and that this do not seem detrimental to the public good.
Reply to Objection 1. There is a place for the judge's mercy in matters that are left to the judge's discretion, because in like matters a good man is slow to punish as the Philosopher states (Ethic. v, 10). But in matters that are determined in accordance with Divine or human laws, it is not left to him to show mercy.
Reply to Objection 2. God has supreme power of judging, and it concerns Him whatever is done sinfully against anyone. Therefore He is free to remit the punishment, especially since punishment is due to sin chiefly because it is done against Him. He does not, however, remit the punishment, except in so far as it becomes His goodness, which is the source of all laws.
Reply to Objection 3. If the judge were to remit punishment inordinately, he would inflict an injury on the community, for whose good it behooves ill-deeds to be punished, in order that. men may avoid sin. Hence the text, after appointing the punishment of the seducer, adds (Deuteronomy 13:11): "That all Israel hearing may fear, and may do no more anything like this." He would also inflict harm on the injured person; who is compensated by having his honor restored in the punishment of the man who has injured him.
Source: Summa Theologica (New Advent)