Upgrading from high sierra to Big Sur.

Yes, plus the 2014 Mac mini can be upgraded to macOS 12 Monterey.

How to download and install macOS - Apple Support

If you have older 32bit software, then you will need to replace it with 64bit software or stop at Mojave.

https://www.stclairsoft.com/Go64/

currydog Said:

"Upgrading from high sierra to Big Sur.: Can I upgrade from High Sierra 10.13.6 directly to Big Sur? Macmini late 2014 7,1"

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For reference...

Upgrading the macOS:

Determining which macOS Upgrades(s) will Install:

I. Verify Compatibility:

A. Start Here: Learn About Compatibility and how to Identify your Specific Mac Model - Apple Support

B. How to Verify:

I Reveal your Model:

What is the Model of your Mac? To find out...

1. Go to: Apple menu
2. Click: About this Mac
3. View: Second Line-Down

then...

II. Compare the Results:

See if the Model you found is shown here:

• macOS Ventura is Compatible with these Computers - Apple Support
• macOS Monterey is Compatible with these Computers - Apple Support
• macOS Big Sur 11 Hardware Requirements - Apple Support
• macOS Catalina 10.15 - Hardware Requirements - Apple Support
• macOS Mojave 10.14 - Hardware Requirements - Apple Support
• macOS High Sierra 10.13 - Hardware Requirements - Apple Support
• macOS Sierra 10.12 - Hardware Requirements - Apple Support
• OS X El Capitan 10.11 - Hardware Requirements - Apple Support
• OS X Yosemite 10.10 - Hardware Requirements - Apple Support

III. If Compatible:

Back Up your Mac First:  Be certain you Create a Time Machine Backup of your Mac, so that way you can have something to restore your Mac from, should anything go wrong with the reconfiguration.

you should

macOS Big Sur is compatible with these computers - Apple Support

You’re welcome.