Using a late 2014 27-inch iMac as a monitor for a Mac mini

Not with Big Sur, no. You don't say which model mini either. Not for new ones.

Review the document: Use your iMac as a display with target display mode - Apple Support

Target display mode is a feature available with late 2009-Mid 2014 iMacs. The display Mac has to be running macOS High Sierra or older and the signal producing Mac has to be running macOS Catalina (ca. 2019) or earlier.

This could only be done with a very few and very specific older iMacs and support was very limited. Read this topic for a 2021 perspective on this: https://discussions.apple.com/thread/252271436?answerId=254300142022#254300142022

and this 2021 post by Allan Jones about software limitations:

https://discussions.apple.com/thread/252344497?answerId=254428494022#254428494022

and read about Screen sharing Share the screen of another Mac - Apple Support

drjerry513 wrote:

Can I use my late 2014 27" iMac with 3.5 GHz i5 chip running macOS Big Sur 11.7.10 as a monitor for a Mac Mini?

Not with Target Display Mode. That feature went away when your iMac – the first 27" 5K Retina iMac – came out. Apple never brought it back on later iMacs, and at some point, they added restrictions such that no Mac released after 2019 or running anything later than Catalina supports using any iMac as a Target Display.

There is a workaround product called Luna Display (by Astropad) that might let you use that old iMac as a second display. You will still need at least one real monitor. The connection is not as good as with a real hardware display; an article on the Astropad site says that Luna Display is not recommended for high motion content (such as you'd get from video editing or gaming), and that there may be lags and artifacts as changes fill in on the display.

So if you go this route, I would not skimp on the real monitor with the idea that the 27" 5K iMac would be the "real" monitor.

The requirements for "Target Display Mode" are here: Use your iMac as a display with target display mode - Apple Support

At quick glance, your late-2014 may be just out of the supported models.