What do you think about me telling my partner to cut off someone she only spoke to because she wanted to start a fling.
Why would you want your partner to cut that person out of their life?
She is a really bad person. She has been doing something very immoral for a while now.
It's important to make sure that you know what her intentions were.  If your partner was seeking to step out of your relationship with another person, then that is cheating and it was wrong for her to do so.  However, she may just be seeking out a friendship with another person.
I'm going to talk to that person and tell her what a bad person she is then.
You still need to make sure that your partner is actually trying to cheat on you. If she really is trying to have another fling, then it might be best for both of you to end the relationship and heal so that you can move on.  However, you shouldn't assume that is what is happening.