If you have a Mac Mini and Siri doesn't work on MacOS Sierra, the first reason might be that there is no built-in microphone on the Mac Mini. The easiest way to capture audio is by using a webcam attached to a USB port.
You have to make sure your audio input is set for the webcam, and not "Line-in" when you are using a webcam ...
Go to System Prefs -> Sound. Click the "Input" tab. Then select your webcam. The webcam might show as "unknown audio device" in the preferences panel.
If you attach a webcam after the Mac Mini has booted, there is a possibility that audio input from the webcam won't work until the Mac Mini is booted while webcam is connected.
Simply reboot the Mac Mini with the webcam attached. Check for success by testing with Siri.
If the audio still doesn't work, there is probably a problem with the webcam. Try another webcam.