No, microwaves do not kill nutrients in food, at least, not any more than other cooking methods (all cooking methods destroy some nutrients).
The faster you can cook your food, the more nutrients it retains. Since microwaving is a fast cooking method, it retains a high amount of nutrients. In fact, steaming veggies in the microwave (an easy task in a microwave pressure cooker with a steamer tray) is one of the best ways to retain nutrients.