Just thought I'd chip in; since there's no way for you to download the Mii Channel since it's not on the Wii Shop, the only thing you can try to delete is the save data. It won't get rid of the channel, so if it's the channel which is corrupted, you'll need to re-format, but if it's a save corruption you'll be right.
Wii Options, Data Management, Saves, Mii Channel, Delete.
Metroid Prime Trilogy
12/09/2009 / Playing Pokemon Heart Gold