There's instructions in the talmud on how to properly deface the statue of another religion. Knocking off the head is preferrable, if that's not possible chipping off the nose is sufficient.

It's not a coincidence that most of the classical statues of the ancient world were defaced in this manner.

The jews themselves avoid having statues dedicated to their god. I suspect this custom originated because they were afraid of a foreign tribe insulting their religion as they insulted others.

In earlier periods they did have statues to their gods.