Mac Mini 2011 freezes and reboots
The image you showed are symptoms of the graphics chip on the logic board failing. 

This requires a hardware repair (replacing the logic board) unless you find a place that would do component level repairs. 

Given it's a 2011 the Apple Store will still be able to help but the cost of the logic board is (last I recall) usually $157.99 Plus tax plus $79 labor. You get 90 days of warranty on the replacement logic board.