How would the function of a animal cell change if the vacuoles were removed?

Usually, animal cells do not have vacuoles. But, when they do, those vacuoles are included in the processes of vesicular transport: exocytosis and endocytosis. Their role is to support that type of transport: vacuoles are storage vesicles for proteins and lipids that have to be containment, before their excretion (through the exocytosis). On the other hand, during endocytosis (materials brought into the cell) engulfed material is also located in that membrane-enclosed vacuole.