I'm going to cut off a friend
For real? What upsets you about this friend?
She is mean to a particular person, if you are mean, you are mean to everyone, don't choose individuals to attack.
Friends  should try to work things out but it is understandable when you can't because the person did something wrong. Otherwise you will keep being angry at them and explode at them.
She will be fine, she has other good friends who support her.
That's good then, you don't need to be present in her life if she caused you harm. Your mental health is very important, and you might thank yourself in the future for making these decisions.