cut (someone or something) with (something)
1. 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.
2. To slice or chop something with a particular tool or implement. You'll only be able to cut that rind with a sharper knife.
3. To add a substance to something in order to dilute it. Be sure to cut that juice with water before you give it to the kids. If the coffee is too strong, try cutting it with cream and sugar.
cut someone or something with somethingand 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.