This is a tough question, because there are no easy answers.
In the first place, it would help you to gain some perspective on how bad things can be / have been for other young people in your situation. I’m not kidding when I suggest that you read books such as White Oleander or even some of the Dickens classics: Oliver Twist, for example.
The reason I suggest this is that if you do happen to take the “emancipation” route, or if your search for assistance through school and government agencies lands you in foster care, you might find out – too late – what it really means to “jump from the frying pan into the fire”.
I’m not going to suggest that you’re just spoiled, a drama queen or a prima dona who thinks she’s too good to get her hands wet in dishwater – but you need to consider the possibility. I know that when I was growing up – and I confess that I had an outstandingly good relationship with both of my parents, I still knew well enough what would trip their triggers and sometimes, just for the hell of it, I would push their buttons and start a fight. I presume that your mother is not on drugs, or an alcoholic or mentally ill (or criminal, or over-stressed because of dire financial straits, or other such issues), which would obviously affect her mental well-being, mood and outlook on life, and I also presume that you’re intelligent enough (and self-perceptive enough) to know when you’re doing things that you know are going to upset her because you already have the fatalistic attitude that “It won’t matter; she’s going to be hateful anyway, so I might as well [insert the action or attitude that you know is going to upset her], just because I want to.”
I’ve raised two kids of my own, and as I admitted above, I do know (and remember for myself) what kids can be like sometimes. I suspect that you already know that there is room for improvement in your attitudes and actions, but you’re looking for an easier answer – which would mean that you don’t have to change your behavior (because none of us likes having change forced upon us) – but there may be forces at play with your mom that she’s attempting to shield you from, too.
My suggestion would be that you approach her at some time when you’re both calm and relatively at peace with each other and just start a dialog with her based on the question, “Mom, how can we get along better?” This absolutely will not work to stop an ongoing fight – it will be perceived as a ploy to turn off what she would feel is her righteous anger and would simply appear to be an attempt at manipulation by you. Trying this during a fight or argument would probably worsen the situation.
If you can start that dialog at a good time, make it a sincere question and really listen to her responses – and then take honest and positive steps to live up to her expectations – then that might be a route to improving the situation. You have to be willing to change the things about you that upset her. When she sees you acting in a more mature and adult-like manner, then would be the time that you could start to negotiate for change in her behavior as well.
Of course, if I’m wrong about my list of assumptions, and she is unbalanced by forces larger than either of you can deal with, then we may need to revisit this question. I’m also making the assumption, like @JLeslie, that she really does love you, but her temper sometimes gets the better of her. I’m not downplaying how bad this may seem to you right now – and I know that growing up with divorced parents can be its own kind of hell, and a sibling who will take advantage of one parent’s preference at your expense adds to your perception of misery – but you are the one who is going to have to make this better.