Unhealthy Relationship?

She is dating you. She cut her wrist. She knew before hand that this would upset you because you care about her. Therefore, she does not truly care about you because if she did, she would not intentionally upset you.

Be straightforward with her. Tell her to go get help and leave her.

I am telling you from experience. She will just continue to hurt you until she gets help. Maybe there is a chance for a relationship after she gets help. You cannot hold a stable relationship with someone who is mentally ill, but you can be there for them.