First of all, it is important to remember that heating with a microwave is a completely different process than that of a heating oven or a gas stove. Typical heating methods include conduction, convection and advection but microwaves heat by realigning the water molecules in food which are essentially polar molecules, to the constantly changing electric field (microwaves). This continuous realignment process causes the water to bump around continuously thereby creating a high amount of friction leading to heating of the material around the water molecules. But does this process destroy nutrients in the process?
Whenever food is heated by any means, whether a conventional gas stove, or a hot plate or even a fire, the food loses some of its nutrients. How much exactly are the amount of nutrients lost depends on how you are heating it, how much water you are adding to it and most importantly how long are you heating it? Well cooked food makes it easier for our digestive systems to handle allowing us to absorb its energy. Cooking with microwaves takes relatively less time, less water and thus we can safely say that fewer nutrients are drained out in this cooking process.
However, a microwave can superheat or overheat your food or can leak radiation due to a faulty door seals causing burns. Contrary to popular beliefs, microwave radiation is non-ionizing , just like radio waves, which means that its less likely to cause damage to your DNA(causing cancer). Radio waves, microwaves, Infrared and visible light all lack the energy to excite electrons off atoms, but UV, X-Rays, Gamma rays, are made up of higher energy photons that can break away electrons from atoms causing ionization. Some foods like breast food are not recommended to be heated by microwaves as they can damage the helpful bacteria present inside in a very short span of time.