[From "Blood Atonement"]

No doctrine of Mormon theology is more misunderstood, and feared, than that of blood atonement. This is mostly due to the apostate, murderous, John D Lee. Who masterminded an attack on a group of people in the southern Utah hilltop called "Mountain Meadow"[…]
Blood atonement is in essence capital punishment. It is an answer to justice. It is a law that is to punish a guilty person for a very serious crime, as capital punishment is in the justice system now. If a man is a murderer, he cannot be forgiven in this life at all, no matter what else he does. He must give his life in an effort, on his part, to atone for his sin. He needs to have his blood actually shed upon the ground as an act of atonement, in an effort of repentance
Blood atonement was also taught by Brigham Young to be necessary for the sin of adultery[…]Once a man is ordained as an elder, and is sealed to his wife or wives by the Priesthood, and then commits adultery, his sin necessitates blood atonement. He cannot become baptized again after that sin, so he must either find his way somewhere else, or atone by giving his life. The same for a woman. This is what “destroyed” is referring to in Section 132 of the Doctrine and Covenants

This is a law of God that the people of ancient Israel lived when there was no other government over them. Achan was the first documented case. Some say that it was observed in the Utah territory during the days when Brigham Young was the Prophet. But when there is another government over the people which govern these things, they are subject to them. So those who want to atone by blood for adultery CANNOT at this time unless the civil government passes the law and administers it

Yea, yea, I bet some of you are saying. Why cant you perform blood atonement that is against the law, if you allow polygny which is against the law? Simple. One administers life, the other takes it