Ignore apps on clone system disk
The cleanest (and safest; see below) solution would be to set up Carbon Copy Cloner to automatically mount the clone disk/partition before the backup starts and unmount it once the backup is finished. See:
https://bombich.com/kb/ccc4/performing-actions-before-and-after-backup-task

Not only would this prevent the problems you have described, it would also protect you a bit better against ransomware, which unfortunately made its appearance for the first time on OS X a week ago, because your backup would only be vulnerable during the daily cloning window and not all the time.

Short of doing something radical such as stripping the executable rights from all your files on the backup disk (which would also break the backup), I don't see how you could prevent applications to be launched from it, and even that might not prevent helper code to be executed by a main application.

What you could do is add the backup disk to System Preferences->Spotlight->Privacy. That would at least prevent you from accidentally launching apps from the wrong disk yourself using Spotlight (or launchers that rely on Spotlight such as Alfred).