Nothing but sympathy, if you have guidelines to follow, talk to the person in private first, reporting something like this can cause major triggers, causing family and personal problems worse.
Don't be the tree hugger type that thinks everything is all going to be sunshine and Roses if you bring it up to them or anyone else.
Make sure they are fine and that you are there to talk or support them.
Just be aware, you pulling them up or talking about it can also set them off.
Me personally (if I was a teacher) as a SH'er, I would just make sure they are ok and they have a free space to talk without judgment or for them not to worry of other people knowing.
If they don't appreciate your concern don't take offence to their 'over' reaction, don't deal with an outburst with logic, they are running on emotion, logic/rational thinking is out the window at this point let them calm first.
At the end of the day, it is very personal and they are emotionally unstable and vulnerable.
teachers are mandatory reporters they have to follow school rules about reporting.
My reaction would be to follow the administration's protocol for these situations.
Don’t speak with the parents... that escalates things. You need to talk with the student in private and see what the best course of action would be. Whether they need councilling or not. Just never pressure them. Only take matters into your hands if you think they are a risk to themselves
Send the student to the school nurse for bandaging. Trust that the school nurse will take care of any other legally required things.
I would be extremely supportive, (I self harm) because anyone who is cutting is going through a hard time.
i would speak with the child's parents and let them know