cut (oneself) with (something)

To cut or gash a part of the body on something sharp or dangerous Here is a sharper knife, but please be careful not to cut yourself with it. Kids, get away from there—you could cut yourself with all that broken glass! Those are kitchen shears, so please don't fool around and cut yourself with them.

cut someone or something with something

and cut someone or something on something

to slice someone or something with or on something. Don't cut yourself on that sharp blade. He cut the bread with a dull knife and crushed it.

cut something with something

to dilute something with something else. They cut the liquor with cold water. Please cut this with some soda. It's too sweet, otherwise.