You say your "school counsellor" .... is this at some sort of post secondary education?

MdngtRain is correct in that it depends on your location and your intentions with the cutting. Generally, if you are not in any immediate threat of danger to yourself or others, then the person with whom you are speaking is not allowed to break confidentiality. That being said, it might be worth a hypothetical conversation with this person about the limitations to their confidentiality. In this way, you can ask them under what circumstances they would be forced to share the details of your conversations, and then YOU can make a choice about what you would like to disclose. Don't feel pressure to tell them what's going on (if you're not comfortable) and they get a feeling like this might be going on as a result of your conversations. It's always your choice.

Also, given that you are an adult, it's unlikely that your mom could "force" you do go to a "mental hospital" as you would need to either admit yourself (given your age), or a higher body (e.g., the staff there, the police, etc) would need to be certain that you were going to kill yourself - and this is substantially different than cutting yourself... it all comes down to intentions.

Hope that's helpful
Jacq