There are lots of products to help get mats out. Cowboy Magic Detangler and Shine is a great one. I use it full strength -- just rub a little on those mats and then you can gently pull them apart with your fingers. I used this when Ben and Sadie still had that fine puppy hair that will mat if you look at it wrong.
I have also read that rubbing cornmeal into a mat will help detangle it like magic! There are many other detangling products -- even human conditioner or spray detanger for kids works on some mats. I would try these sorts of products before shaving it off. Not only is it difficult to shave if the hair is matted close to the skin, matted hair also dulls your clippers or trimmers quickly. Even if you have a professional groomer do it, they may charge extra due to the extra wear on their tools.