You mean blood atonement as in the killing of apostates, right?
I think the evidence is pretty solid that they supported blood atonement, in the sense of executing convicted criminals in a way that spilled their blood (firing squad rather than hanging, for example).
The problem is that the evidence I've seen (and admittedly I haven't looked into it a whole lot, so there's lots out there that I haven't seen) tends to be the murderers themselves saying the order came from higher up, but the higher ups themselves denying it. Of course both sides would have an incentive to lie to pass the responsibility, depending what the actual truth was.
What's the best example of evidence, that shows Brigham Young or Joseph Smith specifically ordering a murder?
I always figured it was because the Book of Mormon was supposed to sound like the Old Testament, and the Old Testament is the same way.
Do you think that Mormons were significantly more violent than Protestants at the same time and place?
Edited to add: I think that both were similar, with the violence gradually escalating from things like mobs and tar & feathering, to frontier-style murders, as the Mormons moved toward the more-violent frontier, so both sides were using their religion (or hatred of another religion) to justify actions that were actually more affected by the larger cultural norms around them.