I think it would depend on the specific local environment. On the space station, the levels of radiation are actually fairly low because it is blocked by Earth's magnetic field. Over 6 months astronauts on the space station are dosed with about the same amount of radiation that we get on earth over 43 years. So higher than normal but completely manageable and mostly safe. Though of course there's always a small probability something important will be mutated and go un-repaired.
However, outside of Earth's magnetic field and without other protection, high energy particles from the sun and even cosmic rays could definitely cause mutations, if not significantly worse damage.
I think it would depend on the specific local environment. On the space station, the levels of radiation are actually fairly low because it is blocked by Earth's magnetic field. Over 6 months astronauts on the space station are dosed with about the same amount of radiation that we get on earth over 43 years. So higher than normal but completely manageable and mostly safe. Though of course there's always a small probability something important will be mutated and go un-repaired.
However, outside of Earth's magnetic field and without other protection, high energy particles from the sun and even cosmic rays could definitely cause mutations, if not significantly worse damage.