I dont know your daughter, but from what you have said here, it certainly sounds like she is being extremely manipulative. She knows how to press your buttons. She is clearly known for manipulating you in situations like this. She continues to do it over and over and in the meantime, you are left with zero control over your teenager (whom you obviously love dearly).
If she is making threats to "slit her wrists" then tell her that, because you love her and want her to be happy and healthy, it is time to seek some help for her obvious emotional problems. I would take her to see a therapist.