Is it forbidden for me to cut ties with a friend who talks a lot about people?

If your conversation with your friend involves backbiting (mentioning people in a way they dislike), then this is impermissible and forbidden by Islamic law. You must avoid backbiting and ensure that your gatherings are focused on goodness and obedience. If she engages in backbiting, you must denounce it, explain its unlawfulness, and redirect the conversation away from forbidden topics. If that does not work, then it is obligatory to avoid such gatherings. If that is difficult or if she does not accept your advice, then leave that gathering if you can. It is not necessary to completely boycott her; rather, you can maintain ties through greetings and similar actions that do not lead to something forbidden. However, if avoiding backbiting is only possible by boycotting her, then there is no blame upon you for doing so, for a legitimate Islamic reason.