How do I stop OS X from treating a SuperDuper image on an external drive as part of my current installation?
Most people I know that keep bootable backups do one of two things:


Do these backups far less often and use Time Machine to keep the most up to date backup.
Script mounting and ejecting the drive as part of the copy process.


The first option works well for a monthly rotation (and just before major updates like an OS update or upgrade) since the bootable image is more about getting running rapidly than needing to have a perfect mirror of everything when your actual data is backed up elsewhere. 

The second option I have seen for people that really despise Time Machine since you will get all sorts of unwanted confusion having two (or more) OS mounted at the same time with Spotlight, App Store Updates and worse mixing up which file should be opened or updated.

Assuming you have already told SuperDuper to not make a fresh copy and instead perform a smart update, you might be in the same boat as these:


Why do apps which are not installed run from an external bootable drive?
How do I make Spotlight stop indexing my Backup drive?
Stop Spotlight from indexing a drive that is regularly unplugged and reattached


The last topic about indexing may also help you if you script the mounting and unmounting as spotlight may want to reindex the drive each time depending on precisely how you have SuperDuper set up.