Mir isn’t in orbit anymore, it was decommissioned and burned up in the atmosphere in March, 2001.
An astronaut, whether in Mir or in the new International Space Station (ISS) receives about 1 millisievert/day (mSv/day) or 0.365 Sv/yr. Normal overall radiation dose for someone on earth is about 3.5 mSV/year. 4 Sv kills most people, 2 starts giving you serious health problems. Note that different parts of your body are affected differently, so a safe dosage for your skin may not be safe for your sex organs. Also, any high exposure increases your long-term risk of cancer, so you may be fine after a 2 Sv exposure in one day but die from cancer 5 years later.
Note that radiation in space is somewhat different than radiation on earth. It’s all “radiation”, but on Earth, heavy particles are typically stopped by the atmosphere. On a space station, much of the radiation comes from “spalling”, where a heavy particle or cosmic ray hits the aluminum spacecraft body and causes a release of secondary particles. Much of the space station radiation is from these secondary particles. Any aluminum-body station (and that’s all of them) has this same problem, so ISS is just as bad as Mir.
Attempts have been made to provide additional shielding using hydrogen-containing materials such as polyethylene. In the ISS, these attempts haven’t been successful.