Q: Does my Mac Mini have an SD card slot?

1. Depends on which year model you have...?

see > How to identify Mac mini models - Apple Support

The early models before and including the Mid 2010, do not have a built in SDXC card slot.

The later models after and including the Mid 2011, have a built in SDXC card slots on the back.

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2. If you have an early model or do not wish to reach around the back of the later models..? 

Most all corded USB multi card readers work with Mac's.  (example's below)

http://www.amazon.com/Speed-Memory-Reader-Writer-Microfiber/dp/B00R07WNRY/ref=lp _516872_1_21?s=pc&ie=UTF8&qid=1450022133…

http://www.amazon.com/Scm-Microsystems-SCR3310V2-Smart-Reader/dp/B001L6OVZM/ref= lp_516872_1_11?s=pc&ie=UTF8&qid=14500221…

You are welcome!

I plug my card reader and other removable USB devices into a self-powered USB hub, that always stays plugged into the Mini. That way I do not have to fumble around trying to plug and unplug things into the back of the Mini.