I'm going to completely shut out my depressed/suicidal ex-girlfriend
Why would you completely shut someone out that is going through a tough time? It doesn't sound like a very nice thing to do.
She's really bothering me with her suicidal tendencies. That's unhealthy and it's affecting me
I understand that you may not have the tools to deal with your ex-girlfriend's depression. However, she is going through a hard time so it may be helpful if you can help her find a support group.
What if I don't care about her and I want to keep myself sane.
This is a lesson in empathy and being there for someone else, whether it is an ex or not. Helping another person when they are going through a tough time is a good way to simply be a good person.