There is certainly much that we do not learn here about the Zoramite religion. Most famously we learn of their rameumptom (an elevated place in their synagogue; Alma 31:21), but we also learn that they “bow[ed] down to dumb idols” (Alma 31:1). Although that doesn’t tell us much, it may be the explanation for the specifics of verses 10 and 11. As part of the explanation for what the coming Messiah will do, Amulek teaches that there must be an atonement, which is “a great and last sacrifice.” Then he tells them what the sacrifice cannot be: “not a sacrifice of man, neither of beast, neither of any manner of fowl; for it shall not be a human sacrifice.”
Why explain what not to do? It is possible that in the acceptance of the dumb idols, the Zoramites had also accepted forms of sacrifice to those idols. Against a Mesoamerican background, the indigenous gods did receive sacrifices of beasts or fowl, and they did receive human sacrifices. These verses make most sense in the context of what they might actually have been doing, rather than a theoretical prohibition of things they had never even thought of.
Next, we have: “there is not any man that can sacrifice his own blood which will atone for the sins of another.” That also fits a Mesoamerican context where the stories depicted on carved stones tell of kings and queens performing sacrifices that would shed their own blood.
In a Mesoamerican context, it would appear that the Zoramites had syncretized their beliefs with Mesoamerican religions, and had accepted many of their practices. Amulek is declaring that those religions practices, even if thought to be similar to the Messiah’s atoning sacrifices, were not the same, and could not provide eternal redemption.