Study after study have shown that spanking and physical violence against children is utterly ineffective. If you have to lower yourself to hitting to win an argument with a child, they have beaten you. I am sorry, but it is what it is. It also fails to teach them coping skills of their own in difficult situations that don't involve violence. Logical consequences have a much, much higher rate of efficacy.
In my high school, there were the kids who mouthed off to teachers to look rebellious or cool or whatever when there were others around. Remove the audience and deal with the kid in a calm and collected manner. Again, if you chokehold a teenage girl and throw her against a wall, you just lost and made her the victim.
This works for a lot of kids but some don't care what you say to them. You have to show them you mean business. This girl wasn't going to listen to reason. I would love to see you deal with a kid like this. I bet you would change your tune pretty quick.