That's exactly what I did. I finished the game as a mage but I missed a lot off fun stuff, such as the dragon armor or the easter egg area and off course a couple of quests.
Now I started over as a fighter (terminator style) and I'm trying to do all the stuff I missed out before. It's quite fun and very different from my first run through DD. It's actually nice to go mental on your enemy with a huge bastard sword instead of hiding behind your summoned legions of destruction and casting hell spikes from a 20 feet distance.