"nick" or "scratch" may work.
Another word for a shaving cut is a nick
another word for cut a little?
another word for carved is cut.
Chop is a kind of cut, generally featuring repeated, forceful short strokes and resulting in many small pieces.
Tmesis
add a letter to mined ad get a word meaning cut to small pieces
Cut-less
break
nick
An unpicker is also called a seam ripper, which is another word for a small tool used for unpicking stitches. You can stab and or cut your finger with it if you are not careful.
A throat slit is when you have a cut. Its just another word for it. But a deeper cut thn a cut....
snap,rip,