I think your Mac mini identifier is Macmini7,1. That model originally came with OS X 10.10 (Yosemite). I don’t know if you can install OS X 10.6.3 (Snow Leopard) on it, but you could try. You may have to erase the drive via Recovery and restore data from Time Machine.
If you don’t have the Snow Leopard installer, you will have to look for Mac users who have a copy because I don’t think it’s available for download anymore. It would be wise to have the Yosemite installer as well, if the downgrade fails. No matter what, make sure you have Time Machine backups.