It wasn't self defense. The incident occured outside, he chose to follow her inside. She was in the wrong initially but she posed zero threat, especially if he doesn't chase her. You can argue that she probably deserved a slap for using racial slurs if you wanted to.
The act is cowardly but it was the reaction that ruled him out for me. He got zero punishment for it, never offered an apology until a PR firm got involved when he got feedback from the NFL. Tweeted about "making 2016 for his haters", egging on people that gave him grief for it. You're not judged by your worst act but by how you respond to them.
For me, Joe Mixon fell short on that front.