For the 2011 Mini (which has only thunderbolt but no USB3, is this correct?), it looks like the only "external option" that will deliver SSD speeds is to go with an external thunderbolt enclosure.
I'm wondering if a thunderbolt dock (with a drive connected via USB3, provided you get a dock which supports booting via USB3) might work? But would actually cost more than simply attaching a thunderbolt drive.