When you cut with an oil-coated blade, you're generally going to remove the oil. It gets wiped off onto the whatever is being cut.
For my carbon kitchen knives, I wash the knife after use with regular dish soap and rinse with hot water. Then I thoroughly dry the knife. After that, I apply some mineral oil to a cloth and wipe the knife with it. It needs only a very thin coat. When I go to use the blade, I wipe it off with a dry cloth. The mineral oil I buy is safe to eat, but I prefer not to add it to my food.