I tend to agree with the comments suggested already in that there's basically two ways forward.
1. Really, and I mean REALLY talk to her.
Seek first to understand. Why is she acting out? You need to get to the truth, and to get there you need to have open honest conversation without fear of repercussion. She may be jealous, resentful, struggling internally. There cannot be any consequences to her saying things like "I just hate you" or something. Does she need mummy daughter dedicated time, a holiday or something? It's clear she's acting out for a reason, but you need to figure out what that reason is.
2. Tough love
Nowadays it's often looked down upon to deliver tough love, but in many cases I believe this is needed. Your job as a parent is to shape this individual into a well rounded young adult, if you think drastic action is needed then go for it. In the real world there are consequences, and i'm not talking about being grounded. Like, if you carry on like this you will end up in jail or dead. Terrifying, but true.
Good luck and if you want to talk further just let me know!
p.s. I would highly recommend two books...
"How to talk so kids will listen, and listen so kids will talk"
"The book you wish your parents had read"