Cut contact.

No.

She over-reacted; you did the right thing. However, realize that if she is suicidal, she is not rational at this point. What she really needs is undivided support and honest communication. Cutting off contact would be the wrong thing to do. You did the right thing, continue down the right path: help her.

As someone who has been suicidal, I know from first-hand experience that when I felt really bad, the worst, I felt entirely worthless and wanted to prove that I was worthless. I did this by being self-destructive, so that I would have proof of my inherent unworthiness. I would purposefully act different from what felt right, from what felt like me, to distance everyone who could help me, to push myself into acting on my feelings.

Don't cut contact. That is the wrong answer. Do what you can to help. That being said, don't let it destroy you. If they are asking too much, they are asking too much. BUT, acting irrational while being suicidal is not a reason to cut contact. That just means they need help. Do what you can.