Radiation will not make you mutate if you suffer it.
However, Mutation can come about in offspring. In some cases of ( I think) lizards) found in cooling water from Nuclear Power stations, cases of animals with the wrong number of limbs heve been found - or even, I believe, the wrong number of heads. These are the offspring of lizards ( or whatever) which have had their DNA damaged by radiation.
The immediate damage done directly by radiation can be cancer. Mutation can only be second-hand.