Brigham Young, the second President of the Church, made these statements in a sermon:
"There are sins that men commit for which they cannot receive forgiveness in this world, or in that which is to come, and if they had their eyes open to see their true condition, they would be perfectly willing to have their blood spilt upon the ground, that the smoke thereof might ascend to heaven as an offering for their sins; and the smoking incense would atone for their sins, whereas, if such is not the case, they will stick to them and remain upon them in the spirit world.
I know, when you hear my brethren telling about cutting people off from the earth, that you consider it is strong doctrine, but it is to save them, not to destroy them. . . .
And furthermore, I know that there are transgressors, who, if they knew themselves, and the only condition upon which they can obtain forgiveness, would beg of their brethren to shed their blood, that the smoke thereof might ascend to God as an offering to appease the wrath that is kindled against them, and that the law might have its course. I will say further; I have had men come to me and offer their lives to atone for their sins.
It is true that the blood of the Son of God was shed for sins through the fall and those committed by men, yet men can commit sins which it can never remit. As it was in ancient days, so it is in our day; and though the principles are taught publicly from this stand, still the people do not understand them; yet the law is precisely the same. There are sins that can be atoned for by an offering upon an altar, as in ancient days; and there are sins that the blood of a lamb, of a calf, or of turtle doves, cannot remit, but they must be atoned for by the blood of the man. That is the reason why men talk to you as they do from this stand; they understand the doctrine and throw out a few words about it. You have been taught that doctrine, but you do not understand it.
[Source: Journal of Discourses, vol. 4, pp. 53-54; also published in the Deseret News, 1856, p. 235 Utah Digital Newspapers page 3, column 3, quoted at Mormon Bookshelf: http://mormonbookshelf.com/wiki/Blood_Atonement]