How can I grate soft cheeses? Sometimes I need to shred a block of a soft cheese such as mozzarella, or cheddar. When I use my grater, the cheese starts to get kind of chunky as I'm grating it. I end up wasting a lot of cheese when I try to grate it.

It never happens when I grate harder cheeses like peccorino. 

Is there a way to grate softer cheeses without ending up with big pieces of wasted chunks? Is there a particular grater that works better for softer cheeses? 

I currently use a mandolin grater, and not a box grater.
I usually freeze mozzarella and then grate it (longer the better, unless you are in a hurry, then 20 minutes or so works OK).  This works very well.  Other soft cheeses, such as those meant to be eaten at room temp, brie, for example, I wouldn't freeze...  Of course, I don't think many of us are grating brie anyway.