From what I've read, the Chiefs were most upset that Hunt lied to them. Now, they aren't saying the details, but my gut tells me when they heard there was an altercation, they liked asked him "did you hit her?" and he said "no", thinking no footage of it would ever come out, nothing could prove he did (shove and kick her). That must have really upset them. My other guess is that they assumed the NFL would suspend him, likely for some time, that they just decided to cut bait, now, instead of just suspending him indefinitely, and hope something reflective somehow came, or spun out of it.
My understanding of the altercation is the girl was one of two hangers on, and after some talk, Hunt didn't want anything to do with them and told them "get out" (of his room). They were upset about it, maybe nasty, and after an altercation between them and others in the hallway, he got involved. She apparently called him something akin to a "f***ing n****r", and after she hit him, he shoved and kicked her. I think most people, which include the Chiefs organization and the league will view this as beyond unacceptable or unnecessary behavior, two wrongs not making a right, and inexcusable and cowardly. As others have said, as nasty as she was, as wrong as she was, he could have easily just stayed away, or even after she hit him, told her what to do with herself and walked (ran) away.
As to the Chiefs, as much as I say running backs can be plug and play, this has to hurt them because Hunt's style really fit their offensive scheme. There's not much indication Ware can fill that void.