Again, The Answer Is No.
We’re confident about what does and not destroy nutrients, and most vitamins are heat-resistant. Even the vitamins that are not heat-resistant, however, are only destroyed by extremely high temperatures, extremely long exposure, or both; there will be minimal loss at the times and temperatures of the home kitchen. Since microwaving typically takes less cooking time than stove-top or other cooking methods, we might even expect slightly greater nutrient retention!
To summarize: microwaves do not destroy nutrients, and the rumor that they do can only be described as a vile piece of misinformation. Cook away with your microwave, and be thankful we have such a wonderful gadget which makes it possible to cook up frozen vegetables in less than five minutes!