OK...that's a whole different question.
Can you image your current drive to somewhere else? Probably. Depends on why and how bad the original drive is failing.
So:
Connect your external drive
Boot from some cloning application. CloneZilla, perhaps
Tell it to clone the internal drive to the external
Power down, and replace the failing internal drive
CloneZilla again, migrate from the external back to the new internal.
Can you clone directly to an external and have it boot? I'd have to actually see someone do that before I would say 'yes'.