Disembowelment is the act of taking the bowels out of a person or animal, or the state of having had that done. It is the noun that sits beside the verb disembowel. You will see it in history (as a form of execution), in reports of violent crime, and in writing about animals. It is a heavy, formal-sounding word for a brutal thing; news writing may choose a plainer medical phrase, because this one is so graphic. There is no light, everyday use. Though actually, people sometimes reach for the verb when they need this noun; keep the -ment form for the act or the event itself.