Is it okay to run two instances of SuperDuper! at once? It's quite easy to start two instances of any app from the command line. In this case:

open -n /Applications/SuperDuper\!.app


However, I know that this isn't always a good idea because most applications are not meant to share resources with themselves. I was hoping to back up two different drives with SuperDuper! (a hard drive cloning application) at the same time. I was wondering if this is safe.
A better question is "can I back up two different drives at the same time?"

If you have 4 drives total, on 4 different connections, then yes. To be clear, there must be 4 physically separate storage devices involved, not just separate volumes. And "4 connections" does not include daisy-chained firewire devices or plugged into the same usb hub (those count as one connection).

Running 2 copy jobs on the same volume is a huge performance hit - drives have but one read/write head so the absolute best you can do is 2x sequential-copy speed. In reality it will be much worse as the heads are constantly going back and forth between the two copy jobs.

Running data down the same wire will similarly eliminate any advantage you gain by running two processes. 

The one exception to the rule is network copies - downloading several files over the internet (different servers) works because your external network connection is so much slower than the internal connections that they never get saturated.