Can I ‘clean install’ High Sierra on my Mac Mini 2012, in 2019, without disc image?

After clean install you will get faster mini even with Mojave, but, by the way:

1) Download High Sierra

2) Create a bootable USB and boot from it

3) Launch Disk utility. There is an icon in upper left corner with menu (show all devices). Erase disk

4) Install OS

5) Enjoy

I have mini 2014 and clean Catalina works perfect.

Another thing to do is check for the possibility of an impending

or already occurring hardware failure, in particular a failing HDD.

How to use Apple Hardware Test on your Mac - Apple Support

It's a simple test and it would be a good thing to know that

at least the hardware is in good shape.

Also, FWIW, I have a 2010 Mini running High Sierra and it is doing just fine.

Macs, unlike Windows computers, don't slow down over time due to 'bit rot'. If your computer really is slower today than it was in 2012 there are several likely reasons:

1. your computer doesn't have enough memory for the operating system, software, and tasks you are using it for today. If you currently use High Sierra, a clean install isn't going to change things if you turn around an install all the same software again.
2. your computer's hard drive is too full. It is a very good idea (and Apple recommended) that you leave space free for temporary files. About 10-15GB is suggested.
3. you have downloaded malware that is stealing CPU cycles
4. you are using a newer and/or higher specced computer elsewhere and have unrealistic expectations for this 2012 model

Before you spend time wiping and reinstalling your software - and possible getting right back where you are now - download EtreCheck, run it, and post the results here. EtreCheck was written by another ASC volunteer to help us see what's inside your computer that might be causing your problems. It is free and won't take much time.