The black, coal-like residue on a cat's mouth is because the cat food it eats is too high in fat. It's just oily residue secreted by the cat. 
How to remove black soot from a cat's mouth:
At this time, the owner can switch the cat's cat food to low-fat cat food. Also, if the cat drinks water from a plastic bowl for a long time, it is easy to cause bacterial infection around the cat's mouth, which may result in black, coal-like substances.