Both fission and fusion give off ionizing radiation. As long as we are talking about life on an earth like planet then we have magnetosphere protecting us from solar wind and charged particles, we have a atmosphere protecting us form gamma, X-rays and neutron radiation, we have (hopefully) Ozone protecting us from UV. If radiation does induce mutations and more of it the faster evolution is… to a point, it would be a detriment to multi-cellular life forms because they need there genetic information to remain stable so that the cells can remain organized and constructive. On a planet with higher radiation exposure then we have the higher life there would most likely have very complex and efficient genetic check mechanisms perhaps multiple gene cross checking, recombination and correction or even more hypothetically triple or quadruple helix nucleic acid (TNA QNA as opposed DNA)
By the way how do you have a fission star? Would need a whole lot of uranium!