Wow. You know, I'm really sorry it's all like that at home. I'm really shocked at how your family treat you and I think it's incredible that you're still fighting strong - still cleaning, looking after your sister, doing well in school. You know how much strength that takes? It needs to change, though. This is no way to live for you and, quite clearly, it's making you really depressed. So much so that you're harming yourself, a definite sign that things need to change. I notice that you didn't really mention your dad in your original post. Is he about? How does he act toward you? See, I'm going to throw out all the obvious suggestions first. If your dad is about and acts in a more positive way then perhaps try having a chat with him? Or another relative, if at all possible? I know suggesting that you go to another family member for help but not actually be of any use to you, but it would probably be the easiest thing to do in this situation. If it's at all possible then, regardless of how difficult it might be to do, please have a think about telling another family member what's going on and how much it's stressing you out. Even if you can just find somewhere else to stay for a couple of weeks. I know it's not a long term solution but for the immediate here and now it'll give you a break, y'know?
What is it that gets to you most? Having to do the housework, looking after your tiresome little sister, or the words from your mother that must really cut deep? Because I think you could cope with the housework and your sister. I think that if you tried to work something out - a routine for you and your sister - then all that stuff could be managed. But your mum, the things she's saying to you, no doubt, really cut deep, hmm? What your mum (and dad, if he says these kind of things too) are doing is emotional abusive, don't you think? They perhaps aren't even aware of what they're doing, but they're making you feel bad about yourself, commenting on you and your abilities as a person and that is emotionally abusive. And it really, really does need to stop.
It's a really tricky thing, though. As I said, your mum might not even be aware that what she's doing is really hurting you. Even if you try talking to her (have you tried before?) it might not click and it might not help. Firstly, I do suggest you go to her, calmly and in a calm environment, and explain how it makes you feel when she doesn't appreciate everything you do, when she says she's going to send you away, when she calls you dumb, etc. Going to her and just trying to chat about it and explain your own feelings is a really good way to go about things in a mature manner. It might not help, but it might, even a tiny bit, and that's what we're aiming for. A little communication between you and your parents. If it doesn't work, all I can suggest are ways for you to cope with all the things they're saying to you. Again, I know it's not a solution of sorts, but coping with it is better than nothing, right? As I said before, just getting away for a bit might really help, if at all possible. All understanding that you are not at fault here. You parents are taking their own issues out on you, in a really bad way, but it's not your fault. I promise. You're doing your absolutely very best with life and that's all anyone can ask of you. Appreciating yourself and what you do for them, y'know? I mean, I have no doubt that your parents love you. Maybe they're just taking you for granted, maybe they have their own issues which can so often get in the way of their capability of looking after their children, maybe... well, maybe anything really.
This really is a difficult position to be in though. How old are you? Something else to hold on to, maybe, is the knowledge that some day you WILL get out of there. Some day you won't be their slave anymore, and they won't be able to throw nasty words at you because you'll be out there on your own, doing your own thing, looking after yourself. I understand I'm not giving you any direct, quick-fix solutions but I am trying to give you things that'll help you in the long term, which can be just as beneficial, I hope.
Your little sister also concerns me. She's really still very young and can be so easily influenced. As you're the person who has to look after her so often, you can help teach her right from wrong in regards to you, y'know? You can teach her how to start doing housework - tidying, or attempting to tidy, her own room at the very least. Teaching her to put toys and papers or whatever away after herself. She's still very young so there's only so much you can do, of course, but you CAN start it and it'll stay with her as she grows older. She needs some consistency in her life, and your mum doesn't sound like the person giving her that. You can, though. I know it must be so difficult looking after her all the time, especially as that's your parent's job and not yours, but sometimes that's just the way things work out. I'll bet you she appreciates it when she's older. She certainly won't forget it, and it'll be you who she looks up to, listens to and admires.
I don't know. It's a huge amount you're having to deal with and only so much you can do. Can you speak to a counselor or close friends about what's going on? Just so you have someone there who is listening to you and what you have to say for a change? I reckon it's so very important that you get those feelings out and you seek out help from people who really care about you. I do think that's important. The cutting doesn't help - it's not solving your problems at home - but I do understand it. And I think one of the first steps to getting over it and coping with life without it is to get help for some of the other issues going on in your life right now. You don't have to tell anyone about the cutting right now if you don't want to, but telling someone about how unhappy you are is important. Hard, sure, but maybe super helpful.
I really hope things work out for you. Really I do. Best of luck to you. Keep pressing on, yeah? It won't be forever.
-------
to turn the darkest room of suffering
to a greater state of pain
don't tell me that's behind you now, don't greet me
don't meet your dying blind