Your vet might be able to use a dental saw. Keep in mind that any clippers used on teeth will quickly become dull and useless for nails. Teeth are brittle, so you can't really cut them. Instead, the goal is to get them to snap off in the right spot. It's best if one person can hold the rat while a second does the dental work.
Some rats prefer one method over another.
If using a towel, wrap it tightly so he can't get his hands out. If using your hands, let the rat stand on his hind legs on a table, then hold the head with one hand, and the rat's hands with your other hand. I find human fingernail clippers easiest to use when only one tooth is to be clipped, or if the tooth is very long. If a pair of teeth need to be trimmed, I prefer the guillotine-type dog clippers so I can cut both teeth at once. You can also use bird toenail scissors or dykes.