Most times when people respond improperly to things it's because of ignorance.
I feel if you tell your parents they will realize how serious the issue is and change. If they knew you cut then they wouldn't have said those things. Your parents care for you and wouldn't say anything to hurt you.
Feel free to
PM/
VM me at anytime if you wanna talk i'm usually always on.
P.S. I'm proud your going to tell them.