Short bio: Computer Scientist, FOSS supporter (read more)
Tux Machines (TM)-specific
There are community instructions on how to upgrade a Mint box in place, rather than doing a fresh install. Basically what it amounts to is: edit your sources.list to use the next generation’s monikers (for example, change all the instances of Maverick to Natty, and all instances of Julia to Katya). Then do apt-get update, and then apt-get dist-upgrade, then apt-get upgrade, then reboot.
Don’t do it. It doesn’t work. At least, it didn’t work for me trying to move from Mint 10 to Mint 11 on a testing machine. I got failures trying to configure the new kernel. The resulting machine still booted, but I had no compositing and no apparent way to get it. I didn’t really care that it didn’t work, because I was just doing it to test anyway.