Yes Shredded Mozzarella cheese can be frozen and by freezing the shredded mozzarella you can extend the shelf life of the cheese.
Although it's best to only freeze shredded cheese including the shredded mozzarella if you plan to only use it for cooking or baking with where the texture and taste change won't be noticed.
When you freeze shredded cheese including the shredded mozzarella cheese the taste and texture can eventually change and it may not be as tasty as before.
But when you bake or cook with the frozen shredded mozzarella cheese you won't really notice the taste change or texture change.
If you freeze the shredded mozzarella cheese you can keep it for up to a year or sometimes longer as long as the cheese has been properly sealed in the freezer.