Can I use a meat grinder to grate cheese?
During my younger days working in restaurants I have grated many pounds of cheese using a 'meat grinder' (or rather the meat grinder attachment for a hobart stand mixer)...I have also used my home Kitchen Aid meat grinder for cheeses (cheddar, jack and mozzarella mostly). So, it depends on the grinder and the attachments you have but yes it can be done. 

You want a fine grinder plate and cold cheese (so it stays together better). You probably also want to be doing a "serious quantity" as the set up/tear down/clean up will be an endeavor. If your having friends and family over for a Mexican Fiesta, perfect. If you are making a quick plate of nachos...OVERKILL.. For a few burgers, do it once and decide for yourself if you want to do it again.


It won't be bad for the grinder
It won't be bad for the cheese
Expect Leftovers...


(note: IMHO near frozen mozzarella for lasagna is a perfect place to use a grinder for cheese...)