It's vital you eat at least that amount each day though. Your body needs a certain amount of fuel just to function normally, if you dip into that fuel to do your exercises then you do risk doing damage to your body? Plus, as RedKoala said, you run the risk of starvation mode where your weight loss will stall (plateau) and you could end up in a cycle of eating less/exercising more to try to get out of it which would only make things worse? Ask at your gym for advice, I've a feeling they would actually recommend you eat more too, but for 300-odd calories I don't think its a big deal? I was told to have a snack which has some carbs around 1/2hr before a workout/exercise, then a high protein meal afterwards to help protect the muscle in your body.
Good Luck!