The 2011 Mac Mini can be made to run Snow Leopard, thanks primarily to the research and work of newfoundglory on this forum.
His work can be summarized in a recent post I assembled:
Yes, you can restore a 10.6.8 clone to the 2011 Mac Mini and it will boot and work.
To get the 2011 Mac Mini to its full speed, efficiency and utilization of such new technologies as Thunderbolt, you have to install the extra software suggested by newfoundglory:
You can read more about these software additions by googling the term: "NFG gnommak Edition Mac mini 2011"
I just did it, but rather than use a clone, I did it the hard way, but a clone would have worked just as well. I used the instructions offered in the link at the bottom of this post:
1. I added a "Snow Leopard" partition to my 2011 Mac Mini internal HD
2. I booted it into Target Mode by holding down the "T" key during reboot.
3. I connected my 2011 Mac Mini in Target Mode by Firewire to my 2007 Mac Mini and installed Snow Leopard 10.6.3 on the Snow Leopard partition on the 2011 Mac Mini.
4. I used the 10.6.3 folder to restart the 2007 Mac Mini and then used Software Update twice to upgrade all of the elements of Snow Leopard.
5. I shut down both computers, disconnected Firewire and rebooted the 2011 Mac Mini into Snow Leopard and it booted and operated.
6. I then installed all of the newfoundglory additions using the NFG installer and rebooted.
7. The link below suggests that to get an external DVD player to properly function in Snow Leopard on the 2011 Mac Mini you must make this change [I have not tried it yet]:
Following Software Update’s final run of updates, I started working with the Mini and everything looked like it was working, including the all-important Front Row. Front Row was able to communicate with iTunes 11.x, so it looked like I was set until I attached an Apple USB SuperDrive and tried to play a movie DVD. No go; neither Front Row nor Apple’s DVD Player application recognized it as a valid DVD drive.
Why was this? After all, the 2011 Mini never came with an internal DVD player. This should have worked; except for the fact that the 2011 Mini was never supposed to run 10.6.8 either. All of the 2011 Macs that ran 10.6.8 were laptops that came with internal optical drives.
What fixed it was some additional driver modification. Using information found here on MacOSXHints, I edited/System/Library/Frameworks/DVDPlayback.framework/Versions/A/DVDPlayback with the 0xED hex editor. What I was doing was updating DVDPlayback‘s definition of an acceptable DVD player by finding the wordInternal and replacing it with External, by searching for (hex)496E7465726E616C and replacing with (hex)45787465726E616C.
https://derflounder.wordpress.com/2013/01/11/installing-10-6-8-on-a-2011-mac-min i/

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