Microwave has less energy than visible light to which we are exposed a lot. In terms of causing cancer, visible light comprised of the colors of the rainbow is much more hazardous than microwave. Ultraviolet rays cause cancer most of the time because they move or excite electrons from their original orbital. An energy of at least 1216 kcal/mole can excite an electron. Once an electron moves to another orbital the atom to which it originally belonged changes. That change is actually an injury.
The best guide as to safety is to look at the energy levels of electromagnetic waves from the cosmic rays, gamma rays, x rays, ultraviolet rays, visible light, microwave, radio wave, etc. in decreasing order of energy level. You may verify these waves and their order, I am writing from memory. You can even get their exact energy level. I have a Hub on why microwave oven is safe for cooking food.