If your Dad used to beat you, your mom and sister, I think that makes him the worthless one, not you. That’s his big big mistake that he’s made, it is nothing to do with the person you are but everything to do with the person he is. Please don’t ever let a horrible thing like that affect your view on other things. I believe there are lots of people who love you right now and so many people who will in the future, people who are in the right frame of mind and know how to treat someone as special as you. Be happy that you wake up everyday. Be happy that you have the opportunity to go out into the world and are able to treat people the right way, even if you did have to experience the wrong. The thing’s we deal with in life make us stronger and who knows, one day you might be able to help someone who is in your situation.
As for the cutting - please don’t. You’ll have a bad enough time dealing with your problems and still trying to cope with what your Dad did, you don’t need scars all over your body aswell. In the long run, you will regret it and it won’t be as worth it as you once thought it was. Try to take your pain out in other ways rather than ways that will stay on your body forever. You can always try writing down your worries/problems on a piece of paper then burning it - I do this sometimes even know and I feel like it really does relieve you as if you’ve literally burned all your troubles away.