how to install Tahoe to an external ssd on a mac mini m

First off is what is the make and model of the external drive.? The reason for asking is that not all external drives play well as external boot drives with all Macs.

With that said, generally the easiest approach is to enter Recovery and use the installer to install macOS on the external drive. You need to make sure you select the external drive as destination. While doing the install with the internal drive selected will not harm anything, it will just be time lost.

The other is to download a copy of the macOS installer and either install from the installer on the internal or create a USB installer and use that.

The other thing to note is that certain features of macOS will not be available when using an external drive. Things like Apple Intelligence and Wallet do not function on an external boot drive.

The other alternative, and most desirable, would be not to external boot at all and simply move all your data to the external drive to free up space on the internal (photos, movies, documents, etc.) and leave the internal with just applications. There are Apple documents that show you how to move the library for Music to the external and the process is essentially the same Movies and Photos apps.

FYI, it is very important to know the exact model of the Mac involved since the process for external boot drives has changed a couple of times in the last few years from the classic older style Intel Macs (T2 Intel Macs, M-series Macs). You can get the exact model of the Mac by clicking the Apple menu and selecting "About This Mac". You should probably always include this detail whenever asking for help online since that information is needed for many cases which is why I'm not including any specific details for installing macOS to an external drive since there are two different answers depending on the exact model of your Mac.

I also agree with the others here that an external boot drive will likely cause more problems for you. T2 Intel Macs and M-series Macs have a lot more potential issues with an external boot drive.

I wholeheartedly agree with den.thed on booting from your current drive and copying the contents of the Photos, Music, Movies and Documents folder to similarly named folders on the external drive.

NOTE: be sure to test the libraries, Photos, Music and Movies, to make sure they work as intended before deleting the contents of the folders on your boot drive.

You can keep some frequently used files on your boot drive.

I've done the same and have named the folders on the external drive Pictures-2, Movies-2, etc. I then went into the Finder's Sidebar settings and unchecked Pictures, Movies and Documents. I then dragged the -2 folders into the sidebar of a Finder window so they would be like the original folders. If you keep some files in the original Folders you can add them to the Finder's sidebar, hence the -2 for those on the external SSD.

Following the above will let you keep all of the Tahoe's features and maintain an 80-100GB free space on your boot drive to facilitate optimal system and application performance.

+1

If you are looking to free up internal storage, move your Photos, Music, Movie Libraries to the 2T external SSD.

Move your Photos library to save space on your Mac - Apple Support

Change where your music files are stored on Mac - Apple Support

Move your iMovie for Mac library - Apple Support

Free up storage space on Mac - Apple Support

Servant of Cats wrote:

If this is an Intel-based Mac mini, it can’t run Tahoe at all. Even the final Intel-based Mac mini did not make the cut.

LOL, I got distracted. Plus the subject line has "mac mini m" where I assume the trailing "m" is supposed to indicate a M-series Mac. Thanks for catching my mistake. I do appreciate being called out for mistakes.

If this is an Intel-based Mac mini, it can’t run Tahoe at all. Even the final Intel-based Mac mini did not make the cut.