If a cat's whiskers are cut what can happen is the cat cannot gauge hole openings and cannot navigate correctly. This is a sensitive area for cats and are needed by cats for everyday survival. The whiskers helps cats to maneuver around objects, such as furniture and can also help keep the cat safe from enemies.
1 Additional Answer
If you cut off a cats whiskers, he could have balance problems. They use their whiskers to feel their way around and this could cause them to get injured or fall off of something.