Does under-eating or over-exercising slow metabolism?

2 diff responses. Overeating can actually stimulate a response from the brain that actually promotes overating. Aerobic exercise and resistance training both increase energy expenditure but this can also depend on intensity. Consuming a low calorie diet will decrease your metabolism so maintaining a nice balance of cardo and resisitance training will help in my opinion. Do not forget about proper rest and fluids.
Starvation. Yes, if you are under eating your body can go into "starvation" mode and store as much energy as possible and reduce metabolism.