It stinks but sometimes it's safer to just shave them out. Mats that are close to the skin and tight are difficult to remove and it hurts your puppy
I suggest buying a mat breaker from PetEdge. It has hooked blades that break a big mat up, making it easier to comb out with a slicker or greyhound. Some hair will come out, but it's better than shaving.
Remember: humanity before vanity.