Ionizing radiation: Radiation that produces ions during interaction with other matter, including molecules in cells
However some forms of radiation can cause mutations without producing ions. For example, UV light cause mutations in DNA without producing ions, the energy is absorbed directly by DNA and results in mutations.
Remember the exposure to radiation is unavoidable. Everything in the physical world contain sources of radiation. This include our bodies, the air we breathe, the food we eat, and the bricks in our houses. Some of this radiation is left over from the birth of the Universe., and some have been created by the interaction of atoms on Earth with cosmic radiation. These natural sources are called Background radiation.
We also are exposed to medical testing, nuclear testing, nuclear power, etc.