Eldrazi Mimic’s ability will overwrite any other effect setting its base power and toughness. Such effects that begin to apply after that ability resolves will similarly overwrite the ability. Effects that modify Eldrazi Mimic’s power and/or toughness but don’t set its base power and/or toughness to specific values will apply no matter when they started to apply. The same is true for any +1/+1 counters it may have.

Use the new creature’s power and toughness at the time the ability resolves to determine the base power and toughness of Eldrazi Mimic. If that creature is no longer on the battlefield at that time, use its power and toughness when it left the battlefield. (Keep in mind that those values may be negative, for example if a spell like Spatial Contortion giving it +3/-3 is what caused it to leave the battlefield.)