Does your daughter have an official diagnosis--not that a dx is the be-all and end-all, but it helps categorize her behaviors and helps direct her therapy. What Bipolar meds did you try? It might be worth it to try again in a very systematic way. Do you know if she was compliant with her meds? Did her blood levels reach therapeutic range?
There is a website by the Child and Adolescent Bipolar Foundation, www.bpkids.org,
that might be helpful to you and your daughter whether she actually has bipolar disorder or not.
There is a book you should read called "Cutting" by Steven Levenkron. I haven't read it in years and seem to recall that it may be a little out of touch with current research about cutting behaviors, but it can give you some good insight into why people self-harm. I did a lot of research on cutting several years ago for a paper I was writing. While many people think that self-mutilation is a direct symptom of borderline personality disorder, I tend to think that it is a maladaptive coping mechanism that can be present in other psychiatric illnesses as well. One thing to keep in mind is that cutting can be an addictive behavior due to the release of endorphins in response to pain.
There is a program called SAFE (Self-abuse Finally Ends) that has been successful in many cases. You might want to look into that. If I remember correctly, the focus is more on developing better coping mechanisms instead of stopping the self-abuse. In my experience, the more attention that is paid to the results of self abuse, the more likely the abuser is to continue. But there are different reasons for self-abuse and different reactions to it. Some do it for attention, some do it to release unacceptable feelings, some do it when they feel they are becoming dissociative...
I work with this population and I certainly feel for you. I hope you can find some better answers soon.