How does it affect the performance if an iMac 1TB internal hard drive is mirrored on an external drive?
A mirrored RAID would operate only as fast as the slowest drive in the setup.  In this case, unless you are using thunderbolt I imagine the performance would be awful.  Another reason not to do a mirror with an external drive (if Disk Utility would even let you) is it'd be too easy have the mirror fail for a number of reasons.

I would use Time Machine to the external drive rather than mirroring.  Remember that RAID is NOT backup!  If you mess something up then you will lose data, a mirrored RAID is not going to save you at all.  Only Time Machine or a similar backup strategy will help prevent data loss.