updating to MAC OS 14.1

Downgrading the Mac to run an earlier version of macOS is no small feat.

It requires completely erasing everything on the computer by reformatting the drive and then reinstalling the appropriate earlier OS. That earlier OS may be downloaded and installed by booting the Mac in recovery mode and leveraging the tools available there.

Another option is to download the earlier OS directly from the App Store and create a bootable installer on a USB flash drive (recommended). This option must be performed before the Mac is erased.

After which you'll need to recover all of your personal files from a backup and reinstall any third-party apps that you had installed.

This can only be done IF the Mac in question is qualified to run the earlier macOS. If the earlier OS you wish to install predates that which shipped on the Mac's original drive then downgrading may not be possible at all.

How to start up from macOS Recovery - Apple Support 

How to reinstall macOS - Apple Support 

Create a bootable installer for macOS - Apple Support

It's usually mush easier to work through any problems one may be having with the currently installed macOS than it is to downgrade a Mac.

Are you experiencing some specific problem with Tahoe?

That's a bit confusing.

There is no such thing as "14.1 Tahoe".

14.1 is Sonoma. 26.1 is Tahoe.

Also what Mac mini do you have exactly?

Unless you have one released before or during Sonoma's life cycle it cannot be downgraded to it.

If you have an M4 Mac mini that cannot be downgraded to macOS 14 Sonoma.