Cutting is a term used in the bodybuilding industry. It is when you diet so that you lose fat by eating fewer calories. However, you are trying to keep your muscle. You would continue to work out heavily in order to drop the weight but keep your muscles. Most of the people who are or have been cutting in order to shed the pounds without compromising the muscle mass do not feel significantly hungry.
Similar to a regular diet, you should be eating in small intervals with healthy nutritious foods. At first, you will feel hungry because your body is not used to eating the way you are eating now. However, over time your body will adjust to the way you are eating and you will not feel so hungry.