What should I do about a Mac Mini whose fusion drive is getting steadily slower and slower?
As you probably know, troubleshooting is a process of elimination and can require quite a bit of patience.

The first things I'd do in your situation are to try booting in Safe Mode and, if no joy afterwards, reset both your NVRAM and SMC.

Boot into Safe Mode

Follow these steps to boot your Mac Mini into Safe Mode:


Fully shut down your Mac Mini
Restart your Mac Mini
Immediately press the Shift key and keep it down 
Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice. Also, it will take longer than usual to boot.)
Use your computer for a while and take a note of what happens (i.e. Are you still experiencing the same issues, etc)
Once you've used your Mac long enough to know if it's working any better, exit Safe Mode by restarting your Mac Mini
After booting up normally, take a note again of what happens (i.e. Are you still experiencing the same issues, etc)


If you're still experiencing problems, reset the NVRAM and then SMC.

Reset NVRAM

Older Macs had what's called Parameter RAM (PRAM), newer Macs use Non-Volatile Random-Access Memory (NVRAM). It may be worth you also resetting this. Here’s how to:


Shut down your machine. Yes, a full shut down, not just logging out.
Press the power button and then press the commandoptionpr keys. You have to make sure you press these keys before the gray screen appears or it won’t work.
Hold those keys down until your Mac reboots again and you here the startup chime.
Let go of the keys and let your Mac reboot normally.


Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

Once you've reset your NVRAM, proceed to reset your SMC as well.

Reset SMC


Shut down your computer
Unplug it from power
Wait 15 seconds
Plug the power cord back in
Wait for an additional 5 seconds
Press the power button to turn it back on


Once you're booted back in, take a note of how your Mac Mini is running and we'll go from there.