Hey Alien,
It's a good sign to want to out yourself to your parents. It's a brave thing to do. If you still go ahead with it, I think you should just tell them the truth--in the end, they'll have a lot to deal with and will appreciate your honesty--as hard as it may be. Another thing...you might want to consider telling someone else that you trust first, that way, you can talk to this person openly and not have to hide it from them any longer. While you may still choose to hide it from your parents, at least you'd still have a relationship with them. Working while they're not home won't solve anything. Isolating yourself from them won't work and will only make them more suspicious. And going away to college won't be a panacea--it won't magically fix all of your problems.
I have been cutting myself for almost 7 years now and I finally decided to out myself because I was tired of hiding my scars. I told 5 people I really trusted and have been working my way out from there. I decided not to tell my mother or grandparents. I'm not ready to tell them and I don't know if I'll ever be. I may tell my mother later (like when I'm 50) but only if it feels right.
I am 21 and am finally moving out. I am moving to go to school, but it is a permanent one. I realized that I could never stop hurting myself if I still lived up here. Moving out will help, but I realize it won't solve everything. I will finally have a space to call my own and will be able to express myself and that will help, but I still need to figure out why I feel the need and urge to hurt myself. I wanted to make some progress on this before I moved, so I have been working with a therapist (once a week, free to me since I am not working and do not have insurance) over the summer. The idea is to have less 'baggage' when I move. What I'm getting at here is that you can't run from your problems--they will run with you and be with you wherever you end up. I am speaking from experience. Moving out may be a good thing for you and therapy at college campuses is actually affordable. If you want to hold off on telling your parents (I am not encouraging this--only you will know when it feels right to tell them), I suggest waiting till college. In college you will have the freedom to find out who you are and to mold yourself into the person you want to be. You can take advantage of the resources available to you (counsellors, therapy, etc) and tell your parents when you have a better handle on the problem yourself. They may react differently if they see that you have a grasp on this and that you're working to stop it. Hope this helps.