Can you self harm without being mentally ill?

The thought of being mentally ill, or having some kind of disorder has always felt wrong with me. Even though I can clearly see that my whole family has a few screws loose.

Is it possible to self harm without being mentally ill? I don’t cut that deep, but I feel the urge all the time. And I’m actively looking for sharper blades to be able to cut deeper.

But that doesn’t make me mentally ill, right?

I don’t know, it would be nice with some other opinions or insights on this.

Sorry if this is badly written, English isn’t my first language and I’m very tired.