An image below of what blood atonement is/was not, though such depictions were common misrepresentations:
Brigham Young taught this principle in the early days in Utah. Brigham was overzealous in some of his preaching, and this appears to be one of those areas. However, don’t forget this concept was never carried out. Not once.
But even Brigham provided two caveats to this idea: 1) this practice would only occur in a pure theocracy, similar to what was practiced in the Old Testament, and 2) the murderer or sinner would have to volunteer for the punishment.
Even the Old Testament contains laws on the books that were never enforced.
Future leaders repudiated blood atonement ideas that were making bad publicity for the LDS Church around the time Utah as hoping to be added to the Union.
Jeff and Latter-day Saints Q and A shares this:
In Mormonism, blood atonement is a controversial doctrine that taught that some crimes are so heinous that the atonement of Jesus does not apply. Instead, to atone for these sins the perpetrators should be killed in a way that would allow their blood to be shed upon the ground as a sacrificial offering.
The doctrine is no longer accepted by The Church of Jesus Christ of Latter-day Saints (LDS Church), but it was significantly promoted during the Mormon Reformation, when Brigham Young governed the Utah Territory as a near-theocracy. Sins that Young and other members of his First Presidency mentioned as meriting blood atonement included miscegenation, apostasy, theft, murder, fornication, and adultery.
Young taught that the doctrine was to be a voluntary choice by the sinner, and only to be practiced under a complete theocracy (which has not existed in modern times). Young considered it more charitable to sacrifice a life than to see them endure eternal torment in the afterlife. In a full Mormon theocracy, the practice would be implemented by the state as a penal measure.
The practice of “blood atonement” was formally denied and repudiated by the church in a statement issued in 1889:
MANIFESTO OF THE PRESIDENCY AND APOSTLES “SALT LAKE CITY, Dec. 12th, 1889. To Whom It May Concern: In consequence of gross misrepresentations of the doctrines, aims and practices of the Church of Jesus Christ of Latter-day Saints, commonly called the ‘Mormon’ church, which have been promulgated for years, and have recently been revived for political purposes and to prevent all aliens, otherwise qualified, who are members of the ‘Mormon’ church from acquiring citizenship, we deem it proper on behalf of said church to publicly deny these calumnies and enter our protest against them.
We solemnly make the following declarations, viz.: That this church views the shedding of human blood with the utmost abhorrence. That we regard the killing of a human being, except in conformity with the civil law, as a capital crime, which should be punished by shedding the blood of the criminal after a public trial before a legally constituted court of the land. We denounce as entirely untrue the allegation which has been made, that our church favors or believes in the killing of persons who leave the church or apostatize from its doctrines. We would view a punishment of this character for such an act with the utmost horror; it is abhorrent to us and is in direct opposition to the fundamental principles of our creed.
The revelations of God to this church make death the penalty of capital crime, and require that offenders against life and property shall be delivered up and tried by the laws of the land.’’ We declare that no bishop’s or other court in this church claims or exercises civil or judicial functions, or the right to supersede, annul or modify a judgment of any civil court. Such courts, while established to regulate Christian conduct, are purely ecclesiastical, and their punitive powers go no further than the suspension or excommunication of members from church fellowship.
[Signed]: WILFORD WOODRUFF, GEORGE Q. CANNON, JOSEPH F. SMITH, Presidency of the Church of Jesus Christ of Latter-day Saints. LORENZO SNOW, FRANKLIN D. RICHARDS, BRIGHAM YOUNG, MOSES THATCHER, FRANCIS M. LYMAN, JOHN HENRY SMITH, GEORGE TEASDALE, HEBER J. GRANT, JOHN W. TAYLOR, M. W. MERRILL, A. H. LUND, ABRAHAM H. CANNON, Members of the Council of the Apostles. JOHN W. YOUNG, DANIEL H. WELLS, Counselors.
“The doctrine of “blood atonement,” then, is based upon the scriptural laws considered in the foregoing paragraphs. The only point at which complaint may be justly laid in the teaching of the “Reformation” period is in the unfortunate implication that the Church of the Latter-day Saints, or individuals in that church, may execute this law of retribution.
Fortunately, however, the suggestions seemingly made in the overzealous words of some of these leading elders (seems like Roberts is hinting at Brigham Young here) were never acted upon. The church never incorporated them into her polity. Indeed, it would have been a violation of divine instruction given in the New Dispensation had the church attempted to establish such procedure.
As early as 1831 the law of the Lord was given to the church as follows: “And now, behold, I speak unto the church: Thou shalt not kill; and he that kills shall not have forgiveness in this world, nor in the world to come.”
Dennis Prager talks about capital punishment for premeditated murder in this video below. Additionally, he enlightens on other Jewish laws that helped introduce much more humane legal practices.