Removing hair mats is fraught with potential complications. Many mats are firmly attached to the skin, so you must be extremely careful not to cut the skin as you cut off the mat. Many small mats can be removed with a thorough brushing. If mats remain, try to make the mat smaller by brushing the hair near the mat.
Once you are sure that the mat can only be removed by cutting the hair, then go for the scissors. Clippers are the safest and best way to remove matted hair. Unfortunately, most people do not own clippers and must make do with scissors. Be very careful. For severely matted pets, it is easier and safer to see a groomer for professional help.