I second calling the police. It is a very difficult thing to do, but really you have no other option, except to throw her out. She isn't controlling herself, your wife can't control her, so someone needs to call for outside help. Your wife has a right to be safe in her own home. But this is in your daughter's best interest too: it is bad for her emotionally to 'get away with' hurting her own mother, and she needs help to stop. It will also, obviously, be bad for her and others if she learns to abuse people, and ends up without friends and relationships, or hurting someone badly...
You ask what will happen if you call the police. That depends partly on how old she is, and how badly she has hurt your wife. If you do not call them until she has done serious harm, and she is older than about 15, then it will be taken out of your hands and they will prosecute. If you call them sooner, they will come, listen to your wife, and warn your daughter, but they will not arrest her unless your wife asks them to. My own experience was that they advised me to press charges on the third occasion.
Afterwards, she will be very angry. My own son kept saying things like "I can't believe you called the police on your own son", and I had to say things like "I can't believe you behaved so badly I had to".
I know half a dozen parents who have done this, and in all cases, it has only taken 1-3 calls before their teens started controlling themselves and stopped being violent.
I agree with others that it sounds like your DD needs counselling/psychological help. But this will take time, and meanwhile your wife needs practical help and protection. Even if there is a 'reason' for why your DD is behaving like this, she still needs stopping, until the time she can stop herself.
Good luck.