They'll need to be educated on depression and cutting so they understand it. It doesn't make any sense to most people. They'll be confused, and probably extremely worried.
Do you also suffer from extreme depression? If so then getting you help for that is what they should focus on. Hopefully they believe in doctors, because being that severely depressed isn't normal. It's a body/mind chemical imbalance problem, and there are medications that can help wonders.
Maybe start by talking to one parent, the one you find easiest to talk to, and tell him/her you've been very depressed and would like to see a doctor about that. That could be a start. Then later when they're over the shock of discovering how depressed you've been, then introduce the scars which are just a symptom of how depressed you've been.
Also learning Mindfulness Meditation may help. Learn to focus your attention. I think that's why cutting works. It focuses your attention on a body sensation, and you can see it, feel it, focus your attention on it.
Try substituting ice for cutting. Put the ice on your arm, or hold it in your hand, and focus your attention on it, how it feels, look at it, watch it melt. In theory this should work. (Let me know if it actually does!)
I suppose cutting can also be an addiction thing, where it's just a learned response that your brain jumps to when it wants to escape stress or depression. You'll need to unlearn that learned response and substitute something else for it; learn a different response to go to. Switching to a different response will take a few weeks of purposeful concentration. You can condition your brain, prepare it by visualizing doing something different, like ice.
Best wishes! Hope you can see a doctor.
psychiatrist = medical doctor
psychologist = talk therapist
They're both useful.