Hi, yes, it’s fine to give degus mint leaves, it can be fresh or dried. Most of the fresh herbs commonly sold in supermarkets are safe for degus. There’s a lot of information degu safe food on degutopia: http://www.degutopia.co.uk/deguveg.htm#VEGLIST and there are also many degu specific forums around. Degutopia’s list isn’t definitive, but it’s useful as a rough guide. There are people who feed their degus a completely fresh diet, although this can be difficult to do if you don’t have a garden or a lot of time. My guys get a mix of nuggets, seeds and fresh/dried herbs, fresh vegetables and unlimited access to hay.
Favourite herbs for my degus are dill and chives, they don’t like rosemary or tarragon which is tougher even though they’ll eat branches. As I’m sure you know, degus are prone to being fussy and changing their mind about whether or not feel like eating something on any given day.