I'd take a look at what you are eating in addition to how much you are eating. A diet consists of many facets, and you are trying to do something that is not natural for your body to do: lose weight. The challenge is to trick your body into burning its fat instead of just the food you consume. The problem is that many times people cut too much of the wrong things and are actually becoming counter productive.
My personal weight loss journey started with an unbalanced diet. The key to the diet was controlling the pancreatic function. There's a number of diets that are similar in nature to what I did, but there's a few principles to glean even if you choose to keep a balanced diet.
- If you don't eat enough protein you will lose muscle.
- Muscle burns fat.
- Fat contains 3500 calories, and muscle contains 600 calories. In blood glucose shortages, you will burn both of these together--guess which shrinks faster?
- Exercise on too few calories and not enough protein accelerates the loss of muscle. Not what you'd expect?
Now, you might need a higher protein than normal while you are losing weight and exercising. So your extra calories have to come from somewhere else.
An ubalanced diet such as Atkins, South Beach, or Ideal Protein (the one I used) are designed to be temporary. In short, you lose the weight, and "phase off" the diet to maintain--which is something your body is really good at doing. They put the body in a state called "ketosis", which is fine for 3-4 month stretches. Essentially, you have very little carbs (less than 40g a day) and your pancreas will switch over to secreting glucogon which is designed to burn fat and convert it to blood glucose. In essence your body is still getting its full supply of calories needed based on your BMR, but the balance is coming from your fat stores. However, if you don't have enough protein on one of these diets you will start burning muscle along with the fat which is not what you want.
The irony is that simple calorie deficits don't solve the problem you want. Low blood sugar makes you very mean and makes it hard to think. Another, often overlooked problem that has the same effect is dehydration. You need to be drinking lots of water throughout the day. It helps with the weight loss, and it helps with the mental clarity.
Certain parts of your diet have minimum requirements, and going below the minimum needed to satisfy a calorie deficit will do more harm than good:
If you eat about four times a day (breakfast, lunch, dinner, snack) or more, it will help you get through the day with a more even temperament. I also recommend getting more calories from vegetables outside your protein source than grains or anything like that.