I used to try to help my parents figure out how to be happier, healthier people. We'd have what felt like productive emotional discussions, I'd think I taught them something, and then nothing would change. The situation drained me, and the effort made me miserable because feeling responsible for their well-being doesn't work. Finally, one tearful, painful evening, I chose to let go of the belief that I could do anything. I realized that on some level, they wanted to be miserable, and if they were going to change, it would be on their terms, on their time line, not mine. When I truly let go of the need to help them, I felt such a sense of relief, and letting go made me a happier, healthier person. My decision to stop trying had no negative effect on them, either. If anything, ending the pressure to change allowed them the freedom and space to eventually make small changes on their own.
You could do an experiment: For a period of time, say three months, stop trying to save her. Let go of believing that you can change her. Accept her as an angry, disturbed, difficult child and decide there's nothing for you to do about it. Provide material needs: food, clothing, shelter. Provide structure and boundaries: bed time, wake up time, going to school, meal times, homework times. Refuse to react to bad behavior. Give gentle, positive attention when she's reasonable. Ignore outrageous accusations and comments. At the end of the trial period, you can choose to continue in this way, modify the boundaries, go back to what you were doing before, or try something new, but during that time, truly let go of the need to make something happen.