This one was pretty easy, as the working solution for me was available directly from Miro Forums. After shutting Miro down (or rather, after it has shut itself down), do:
cd ~
rm -rf .miro
rm -rf .gconf/apps/miro
sudo apt-get remove sun-java6-plugin
Obviously, this is not a good solution if you need to use Java on the web. For me it’s not a problem, since I like to have the Java plugin disabled anyway, for security and speed.