Headphone jack on my Mac Mini doesn't work. I trouble shoot it with 2 different devices.

Hmm... at this point it is hard to tell if it is software or hardware related.

On the Software side,

1) restart the Mac Mini and try again.

1) test in Safe Mode, as per > How to use safe mode on your Mac - Apple Support

2) reinstall macOS over the current version , as per > How to reinstall macOS - Apple Support

On the hardware side,

1) make sure the plug is fully inserting into the headphone port.

2) maybe try a short headphone splitter or adapter to see if that works.

3) make an appointment at your local Apple Store or AASP and have it checked out.

Also note, you can by-pass a bad or broken headphone port by using a USB to Audio adapter.

What year model is your Mac mini?

Identify your Mac mini model - Apple Support

What type of audio devices have you tested in the headphone port.

(headphones, buds, a headset, a speaker system, please give more details)

Are you saying, it is the headphones that are not working properly?

If so, what headphones or headset are you trying to use?