How do I back up both internal SSD and external SSD to a single external drive?

From time machine system preferences simply remove the external drive you also wish to backup from the list of excluded locations.

The only restriction is the external SSD must be formatted APFS to be eligible for including in a time machine backup. Time Machine will not backup EXFAT drives.

I don't see why not. That's been possible for a long time. Perhaps they thought that you want to backup the backup drive? That won't work. But you can backup an external drive with files and your internal Mac to a separate external hard drive.

Personally, I backup my photographic files completely separate from Time Machine system backups and do not use Time Machine to back them up. Reason there is no "restore" process needed if when getting a new computer or if repairing a computer it is just a simple plug it back in.

Also, since there is nothing "special" in the storage of the photos, you can simply access anything in the backup by just a simple file search and copy.

There are many apps and some are free that can do basic file backups on a scheduled basis without any need to use the apps to access the files.

ReneWMA wrote:

I had a thought after this post that I could also just back up the photo external drive to iCloud as I have plenty of room there and I"m already paying for it.

iCloud is not backup. It's designed to sync files between multiple macOS and iOS devices. Any change on one device is immediately reflected in iCloud and the other associated devices. Advice - don't use it with the idea that it's backup.

ReneWMA wrote:

So now looking for alternative software that with back up both the internal storage on the Mini Mac AND the exertnal SSD to one other external Hard Drive. Thoughts?

I use CarbonCopyCloner for all my backups. Great product, feature rich, up to date. I have used it for many, many years on all sorts of different Macs and versions of OS X/macOS. It has never failed me.

ReneWMA wrote:

Hi, This is the OP. After getting my new Mini Mac and getting everything going, I turned to setting up my two backup systems. The cloud based backup with Carbonite went well after few small hurdles; but then I was having trouble getting my new hard disk backup to connect to the Mac. Called Apple support which resolved the problem, but then, despite assurances here and elsewhere on line, when asking Apple Support about backing up data I kept on an SSD external drive in addition to the internal storage on my Mini Mac using time Machine, I was told that is not possible with Time Machine because of the way Time Machine worked.

So now looking for alternative software that with back up both the internal storage on the Mini Mac AND the exertnal SSD to one other external Hard Drive. Thoughts?

I just use Time Machine. It backs up my Mac and my external drive to a second Time Machine drive.

You can back up your Mac and the external drive using Time Machine just as you have been doing.