Yes! Your system can support two SATA HD or SSD drives!
Here is the kit you need: Mac Mini Dual Drive Kit which gets you the needed parts and tools to put in the second drive. And here is the IFIXIT guide you'll need to follow: Installing Mac Mini Late 2012 Dual Hard Drive Kit.
Are you sure you got the Macmini6,1? I suspect you got the Macmini6,2 Mac mini 2.3 GHz i7 (Late 2012) as it was the first Mac mini model which offered a Fusion Drive. In this series Apple used a 2.5" SSD.
If you got a newer 2014 then you'll have issues as it can't support two SATA drives. Instead it supports one SATA drive and one PCIe custom Apple blade drive. Here's the IFIXIT guides for this series: Mac Mini Late 2014.
If you review this Mac Mini Late 2014 Teardown jump to Step 5 while not present in this system the area just behind the fan is were the Blade SSD would be which you can see in Step9. In the 2012 models this would be a 2.5" HD or SSD. You may want to pop the bottom off to double check what you really have here.
Its also possible someone created their own Fusion Drive setup as well.