Hi
I would say that a lot of what you describe is 'normal' teenage behaviour - pushing you away, arguing, being defensive, cutting off, being moody, mood swings, impulsive behaviour etc. She is trying to find who she is and this involves a great deal of experimentation, impulsive behaviour and mistakes being made - all adding up to your previously lovely daughter becoming a monster overnight.
They say the teenage brain is not fully developed and is undergoing many changes hence the inability to think things through and make rational decisions.
However, as well as being a mother of a truly awful 15 year old daughter (who has just had to go to live with a friend for a month to give us all a break) I am a Community Mental Health Nurse. I would be concerned about the self-harm and the violence toward you. It sounds as though she needs someone to talk with and sounding out your GP is the first port of call. But, I agree with the other posts, if she does not want to follow anything up you cannot force her.
It might be worth looking into what they offer at school in the way of peer support and other counselling type services - again she might not accept support but it is a possiblity.
Also, look at the positives, if you can!!! She does not smoke, drink or do drugs.
Overall I think your best options are to look after yourself, seek out support for you, read about teenage behaviour, talk to Parentline, get a break if you can and let her know that you are there for her when and IF she wants it. I certainly don't think it sounds as if being more firm is the answer, and you sound lenient enough.
She WILL make mistakes and mess things up, let her know that you will still be there for her when she has to clean up the pieces.
I really do feel for you, I have been in tears about my daughter this weekend and feel I have lost her also.
Sarah