Mac Mini (2014) External Boot Drive

1. Under Big Sur -> go to https://support.apple.com/en-us/HT211683 and follow the direction to download High Sierra 10.13.
2. Please do not install after download is completed.
3. Get an USB thumb drive (I think 8gb will do, but stay in safe side, try 16gb). Using direction from here: https://support.apple.com/en-us/HT201372 to make a bootable thumb drive.
4. Shut off the system
5. Plug the thumb drive and external drive (intended for Sierra), then turn the power on while holding "option" key. Special Note: try to use wired keyboard due to Wireless keyboard's Bluetooth latency connection issues.
6. Choose to boot from USB drive -> then do all the routines (erase/partition the external drive, under disk utility) and install 10.13 in the external drive.

Additional Note: Since Big Sur, I no longer can use "System Preference" ->"Startup Disk" to switch between Mojave and Big Sur.

To avoid any headache, I have to use "option" key while booting up system. You will also get some "incompatibility" warning when you boot into 10.13 High Sierra (mine is Mojave) -- just ignore that. I treated both systems (even under the same machine - 2015 iMac 5K) as independent from each other.

I want to clarify:

Please set the default boot drive at Big Sur, and use boot option (by holding "option" key) to choose "High Sierra" when need it.

When boot into High Sierra - the MacOS will have trouble to read Big Sur data (on the other drive) and will display "incompatible" warning alike. BY ignoring it, you just go on for what you need to achieve under High Sierra.