How do I install macOS Catalina on an external drive?

Shinehah wrote:

I have a Mac mini that has run out of disk space so that I can't install much else or update to a newer macOS.

Is there any way I can cause my Mac mini to run off of my external drive so that the external drive is the startup drive and runs the operating system?

What is the issue...?

reference—

If you can’t install macOS on an external disk

https://support.apple.com/guide/mac-help/if-you-cant-install-macos-on-an-external-disk-mchlp2967/mac

If you are running out of disk space, you are smart to add an external drive which you can install an operating system on. It's easy to do. Go to the link below and download the installation file. Be sure to use Safari as other browsers may not work. When the download is completed, you will be prompted to select where you want to install the OS. Just select the external disk. When the installation has been completed, that drive will automatically be selected as the startup drive. Before doing the download, I would make sure that the new drive is formatted the same as your computer's HD is. Last, if possible, use a wired Ethernet cable to connect to your modem. That will ensure that no data is lost during the download.

Catalina

You can obtain a much larger external drive. For this, it should be an SSD, otherwise speed will be poor. Format it GUID APFS. You can then use SuperDuper or Carbon Copy Cloner (or other similar tools) to make a bootable "clone" of your internal drive on the external drive. Boot from the external drive by holding down the option key when booting to confirm that it starts from the external and everything should look just like it did on the internal drive. All files should be there, except now you will have lots more free space. You can continue to work from the external drive and change System Preferences to make it your regular boot up drive.

At some point, when you have decided to make this change a long term one, you should regularly start backing up your external boot drive that also has all your files. The internal drive can be used for miscellaneous storage after that. It might be useful to keep the internal drive bootable in case you need to return to it for troubleshooting purposes.

If you want to keep all your user files on the internal but boot from the external, that requires more work to configure it that way. The simplest way is to do what I describe above. Making backups regularly of whatever drive your important files are on is essential.

A third approach is to simply get a larger internal drive for your Mac mini, if that is possible.