It's not so much the mites causing the cuts, the mites itch and the rats scratch themselves to stop the itching and can damage their skin in the process. If you look on the skin behind their ears you might see tiny little scabs from the itching. It is easier to see to the skin if you blow gently on the fur to part it.
If you do see them itching excessively they should see a vet for a mite killing prescription... It is very dangerous to use over the counter flea and mite powders or sprays on rats, but your vet can give you a safe one.
In the meantime, keep their cage clean so that the cuts can heal..