cut (oneself) on (something)
To accidentally cut or gash a part of the body on something, typically a sharp object. We came back early because Jeff cut himself on a shell at the beach.
cut something on something
1. to slice something on or against something, accidentally. I cut my finger on the knife. Maria cut her foot on the broken glass.
2. to slice something that is lying on something else. I cut the tomatoes on the cutting board your mother gave us.
cut oneself on something
to slice one's flesh with something accidentally. Careful, you will cut yourself on that knife. Careful! Don't cut yourself on that broken glass.