Ionizing radiation does exactly that: it removes electrons from atoms and creates ions. This means that molecules (which are atoms held together by sharing electrons), are broken apart.
Since all our cells are just giant collections of molecules, knocking electrons off breaks apart critical items like proteins. There are different forms of ionizing radiation: photons (gamma rays, x-rays), neutrons, alpha particles etc. Think of them as bullets flying around that hit chains, breaking links.
As to why it makes you tired, I can’t say. It must damage certain tissues that are involved in processes that regulate how much energy you have.
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