I'm not sure, given what you've supplied. It's not something we're aware of in the current version (v1.2 had an issue where it would crash on launch if there were two volumes named the same thing under OS X 10.2.8, but I assume you're running the new version).
You should find a crash log in ~/Library/Logs/CrashReporter/SuperDuper!.crash.log. Could you send that file to
support@shirt-pocket.com? I'll take a look and see what I can see.
Thanks, and sorry for the problem!