You can freeze Mozzarella and it will be just fine.
However do note that when you do freeze Mozzarella the texture of the Mozzarella cheese will change and the taste of the Mozzarella may change a bit as well.
However if you're using the Mozzarella cheese that you froze for cooking or melting then the texture and taste change may not be noticed.
I freeze some Mozzarella cheese and have kept it the frozen Mozzarella cheese for a year and it's been just fine but the taste had changed as well as the texture.
It does not mean the cheese has gone bad but it just means the taste is not as good.
Mozzarella cheese is best eaten and enjoyed fresh and not frozen but it's okay to freeze Mozzarella cheese and any other cheeses as well.