Cravings while cutting are mostly psychological, it's hard to beat them. There is no easy way to stop cravings - which is why getting ready for a contest isn't done by many. You have to learn to ignore the cravings, or find a way around them. For example, if you crave sweet things, try SF FF Jello. Or Yams with cinnamon and spenda on it. If you crave crunchy, try celery or similar crunchy (low cal) veggie.
Gum is used by many to help control cravings, like you said.
Also, you might want to look into splitting up cheat days/meals. Instead of having a whole cheat DAY, split up that day into 2 separate meals. Then, you can have a cheat meal 2x a week (for example, cheat lunch Tuesday, cheat dinner Saturday, rest of week clean). This might help cravings since you are cheating more often, but with LESS food.
You are going to have cravings. They will not go away. A cutting diet is EXTREMELY restricted, and basically, just not normal. You just have to teach yourself to push through it.