Yesterday a woman brought her 10 month old Persian cat in as a minor emergency. He has long hair that had become matted and she was trying to get out a very tight cluster of hair on the inside of his left thigh. Unfortunately her scissors were very sharp, she got too close, and cut right through his skin. The story turned out okay, but she learned a hard lesson. After an hour and $240 the nearly two inch long laceration was sutured close and the cat was sent home to heal.
I see this happen from time to time and the story is always the same. The long-haired pet developed mats and the owner was trying to remove them with scissors. In these cases the mats are tight and close to the skin, making it difficult to remove the hair. Thankfully these are minor injuries that don't bleed as much as would be expected, but they still cause pain, can be a risk of infection, and require stitches. And it's actually pretty easy to avoid the problem.
Don't use scissors to remove matted hair.
Now you don't need to go to a groomer, though that may be the best option and will certainly look the best. Clippers with a #10 or even #40 blade will get through and under the mat much safer. Even if you don't use them properly, usually the worst that will happen is minor skin irritation and abrasions, certainly better than a long cut. These clippers are sold just about anywhere that sells pet supplies, and in a pinch you can even use a beard trimmer. The most important thing is that you don't put a long, sharp blade that close to the skin unless you're an expert.
A simple solution to a problem that should never happen.