If your Mac Mini has Catalina installed, boot Catalina first, reboot in recovery mode and start Startup Security Utility.
Change the T2 settings to Medium Security (Allows any version of signed operating system software ever trusted by Apple to run), and allow external booting.
View attachment 871398
Now you can install Mojave on an external drive via USB stick, or reformat the internal drive (mandatory with APFS!), and install Mojave.
- macOS Mojave direct link:
https://apps.apple.com/ch/app/macos-mojave/id1398502828?mt=12
- If it doesn't download the full installer (6 GB), use the Mojave patcher only to download the full macOS installer:
http://dosdude1.com/mojave/
- Creating a bootable USB stick with Mojave installer:
https://support.apple.com/en-us/HT201372