First, let me express my empathy for the pain you have been experiencing this past year. Depression often starts as an invisible wound, and you, like many others, have found that it can lead to a visible wound; the cutting. Second, let me congratulate you on seeking advice on what to do next. Tackling depression head on will help you begin to gain control of it, rather than it maintaining control over your thoughts, feelings and actions. Third, your instincts are completely on target. Telling your parents and getting help is definitely in order. I am very glad that you are gearing up to do this.
Let me suggest that you simply begin to tell your story. Pick a time and place that you can speak to them with some privacy and some “space” to shed some tears (maybe in the early evening at home, not on the drive to school on a Monday morning). Start wherever the beginning seems to you and describe what you have been experiencing—the negative thoughts, the unpleasant feelings, the physical symptoms (this may include some combination of changes in your sleep, your appetite, your ability to concentrate, your energy level). Sometimes depression begins after a loss or disappointment, sometimes it just starts “out of the blue.” Feelings simply are, they aren’t right are wrong, they are just there. Explain some of the strategies you have tried to make the depressed feelings go away (I bet there was a long list before you turned to cutting). Tell your parents that you realize you can’t fix the depression on your own and that you want both their love and support and professional help to feel better. I predict that doing this will set you on the road to recovery.