This isn't actually true for all foods. Carotenoids, for example, which are very important antioxidants, are increased by cooking. These are in all colored veggies. Cooking doesn't deplete minerals at all. Overcooking might decrease some vitamins, but not very much; what it destroys most are enzymes, which can only be found intact in raw and fermented foods. As to microwaving specifically, I don't know.
Yes, any form of heating veg, fruit or meat will deplete the food of their vits and minerals.... thats why it's either best to gently steam or eat raw.