Before shredding certain types of cheeses, chill them a bit in the freezer.
Freeze The Cheese
Semisoft cheeses such as Monterey Jack and mozzarella can be difficult to grate because the cheese often sticks to the grater and comes apart in chunks. Cold cheese is easier to handle; put the wrapped block of cheese in the freezer for 15 minutes before using. Don't leave it in there much longer, though; the freezer's dry air will sap the moisture from the cheese, making it crumbly.