The energy of a photon is proportional to frequency. Gamma-ray frequencies are 10^10 higher than microwave frequencies (that's one, followed by 10 zeroes!). Microwave frequencies correspond to rotational frequencies of molecules, which means that all they can do is heat molecules up if they happen to have the right frequency (that's how a microwave oven works).
Gamma ray photons have energies sufficient to break and rearrange chemical bonds in random and harmful ways. They can shake-and-bake DNA, which can cause cells to die or become cancerous, etc.
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