If repeated keystrokes/trackpad clicks won't wake the computer back up, then it's probably gone into a deep sleep. Even if it's still cloning, you may not feel confident about the trustworthiness of the clone. Better to scrap this job, and start from scratch once you've configured the computer to give you better information.
First, make absolutely sure that you're doing this clone attached to an AC charger. If you're doing it from a battery, it's powering both the laptop and the second hard drive, and cloning is a power-intensive operation. If the battery drains before the clone is completed, then you'll have to junk the clone.
Do a force shutdown by holding down the power button. Then start up again, open Disk Utility, reformat the hybrid drive to clean up any problems that may have cropped up.
Next, you configure the laptop so it stays awake at full power, so you can keep track of what's going on. Open System Preferences>Energy Saver, click on Power Adapter, and change these default settings:
Set "Computer Sleep" to Never
(optional) Set "Display Sleep" to 3 hours or Never
Uncheck "Put hard disks to sleep when possible"
The Sleep functions kick in when the computer decides you haven't interacted with the computer for some period of time (the default is 15 minutes). The definition of "interact"differs for different operating systems, but it's usually connected to the use of keyboard and pointing devices. System level activities such as the copying utility behind SuperDuper usually won't prevent sleep. A lot of user applications don't prevent sleep, either; I've seen display sleep when I'm watching streaming video, since I'm not clicking on anything.
Once you've reset the Energy Saver preferences, then you can take another shot at cloning your hard drive. Once the clone is complete, you can reset the Energy Saver preferences if you like (and change them on the clone, too, as the clone will duplicate the Energy Saver preferences that were in place at the time the copy was made).