If someone is found guilty of killing another person, the courts may not waive the penalty of execution that he has earned. Similarly, if one person cost another a limb or an organ, the courts are not permitted to waive the financial penalties that the guilty party has to pay in restitution.
The basis of this mitzvah is to remove evil from our midst. If we allow violent acts to go without consequences, people would inevitably eat one another alive. The logic of “the damage has already been done” does not reflect justice. Sometimes mercy is misplaced and leads to greater tragedy than being stringent. (See, for example, when King Saul took mercy on King Agag of Amalek in I Samuel chapter 15. This misplaced act of compassion nearly led to the destruction of the entire nation in the time of Esther at the hands of Agag's descendant, Haman.)
This prohibition applies to the courts in Temple times when such cases were tried in beis din. (Even outside of Israel, the courts are obligated to enforce the legal penalties to the extent they are empowered.) This mitzvah is discussed in the Midrash in the Sifre and is codified in the Mishneh Torah in the twentieth chapter of Hilchos Sanhedrin. It is #279 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos.