It depends on where you live, the severity of the cutting, your intentions with it. Generally, in the US, they cannot break confidentiality unless they deem You a danger to yourself or others. You can always ask your counselor about the bounds of their confidentiality, what would cause then to report anything against your wishes. You don't have to give details and they can't report you to anyone for asking about how they handle disclosures.
I have seen different reactions from different counselors. My high school counselor did not tell my parents without having conversations with me about it. None of my therapists ever disclosed without talking to me first and getting permission. Even when I was hospitalized, we had conversations about going to the er and voluntarily getting help when needed. But your best bet is to ask your counselor about their confidentiality policies. They can differ among agencies, regions, and parts of the world.