Yes, mayhem is a tort, reaching back to the Coventry Act of seventeenth century England. But, be honest, you probably clicked on this link because of a Sons of Anarchy episode? Regardless, while mayhem is a valid common law tort, it has effectively been subsumed into the tort of battery (though in many states it remains a distinct and separate felony criminal charge with a higher sentencing range than the criminal charge of battery).
Mayhem is distinguished from “mere” battery by the requirement of disabling, disfiguring, or mutilating damage to another. The elements are:
(1) Defendant acted with intent to disable or disfigure another; and
(2) Defendant cut or mutilated the tongue, eye, ear, nose, lip, limb, or other bodily member.
However, any damages that can be pleaded or recovered for mayhem can—and should—be simply sought through a civil battery claim (unless you're trying to win Tort-BINGO and are just missing "mayhem"). If you think you have a common law claim for mayhem, hopefully the police are already involved. If not, call them. But it’s an interesting and arcane bit of historical trivia none-the-less.