Mac Mini and 2014 27" iMac

The latest Mac mini (M1) can't use a 2014 iMac as a display.

Use your iMac as a display with target display mode - Apple Support

"The other Mac that you're connecting it to must have been introduced in 2019 or earlier and have macOS Catalina or earlier installed."

The latest Mac mini can't run macOS Catalina or earlier"

ExPort1 wrote:

If your iMac is running macOS High Sierra or earlier, yes, it's possible. Read this guide for more info.

WRONG!

No Retina iMac can be used as a display!! Only mid 2014 (which is a 24" not Retina iMac) could be used or older.

In addition, no Mac from 2020 onward can use an iMac as a display, especially an M1 MacMini!

No this is not possible

If your iMac is running macOS High Sierra or earlier, yes, it's possible. Read this guide for more info.

Before you buy a new monitor, try downgrading your iMac. Downgrade your iMac to the oldest compatible version using Internet Recovery.