Teachers and members of staff have something called a "duty of care". This means that if they suspect self-destructive behaviour, such as self harm, they must report it to a senior member of staff, or, if they are the senior member of staff, they need to take action. They work on risk scales, if you will...
Low/medium risk:
*Little/non-fatal/not "serious" self injury
*Little/no history of self harm
*Manageable stress levels
*Good work ethic at school.
The student is likely to be referred to a school counsellor to talk their problems over, staff members associated with the student are informed so they can be on the look out for any more possible incidents of self harm. The student is unlikely to be referred to outside sources of mental health care.
High risk:
*Potentially serious self injury
*Long/on-off history of self harm
*Excessive levels of stress
*Lack of interest in school life.
The student will be encouraged to speak to a mental health worker at a hospital, the school will work closely with both the student and the family of the student to make sure the student is as comfortable and happy as possible in the situation they've found themselves in.
In terms of personal levels, teachers will not judge anyone who self harms. That would be in breach of their code of conduct and duty of care. Self harm is a mental health issue. Judging or shunning a student who self harms, or has self harmed, is disrespecting the rights of a person with a mental health problem. I hope this answers your question.