Doctrines of Salvation 1:133; “The Latter-day Saints believe in the efficacy of the blood of Christ. They believe that through obedience to the laws and ordinances of the gospel they obtain a remission of sins; but this could not be if Christ had not died for them. If you did believe in blood atonement, I might ask you why the blood of Christ was shed, and in whose stead was it shed? I might ask you to explain the words of Paul, “Without shedding of blood is no remission.””
Hebrews 9:13-14; “For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: 14 How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?”
They do not believe in the efficacy of Christ or they wouldn’t add works. The shedding of blood was what God demanded as a covering of sins in the OT. Jesus fulfilled that and then this promise went even further with the Unblemished Lamb of God. Your sins aren’t just covered, they’re washed away and forgiven forever, but it’s through His blood not ours.