The offering of animal sacrifices was a prefigure of the Church’s offering of the Holy Sacrifice of the Mass. Once the real thing came around, there was no longer any need to follow the prefigures of it as they were in the Old Testament. Many of the practices of the Old Testament pointed toward Christ Who was to fulfill them. The disciplines and rites of adoration changed, but the doctrines stayed the same and were added to according to the deposit of Faith from Christ. For example, the doctrine of the Holy Trinity was added to the belief of one God.
I don’t know much of the Mormons, but I am assuming that they changed their doctrines and in this way changed what they believe. This is different because Christ fulfilled the Old Law and added to it more divine revelation, only changing certain practices, while the Mormons made up doctrines and then altered them.