Did you do a normal install of OS X on that Mini? Or did you do like a power-user install and deselected printer/scanner/etc. drivers? I know OS X comes bundled with a lot but it might be missing it for that particular one. Just a thought.
Go to Print & Scan in System Preferences, see what you can do in the "scan" tab. I have not installed the HP software for my USB-connected all in one, just used spotlight on a lark and was very pleased to not have to download and install 300+MB of HP garbageware.
It's worth a try.
Go to your apps folder and try scanning with image capture.
Worked for me.
Go to Print & Scan in System Preferences, see what you can do in the "scan" tab. I have not installed the HP software for my USB-connected all in one, just used spotlight on a lark and was very pleased to not have to download and install 300+MB of HP garbageware.
It's worth a try.