Radiation creates free radicals which are highly active chemical compounds. These radicals cut the DNA spiral. The aim is to create multiple cuts so that the cell is unable to activate its repair mechanisms.
One example of this is the background radiation on the earth, which is the most important mutation factor known. At the same time radiation may produce new variations of life. The multiple cuts in combination with the repair mechanisms may create new variants of life. Most of these new forms of life are not viable, but now and then something new and viable is created. Without background radiation there would be no life on earth and no continued evolution of life!