Can I clone my startup disk to another SSD to run macOS Mojave and upgrade my startup disk to a newer macOS?

Off the top of my head I can't find a way to do that in the direct manner you describe, but I believe if you were to install Mojave on that 1 TB SSD, boot from it, and then use Migration Assistant to migrate selected broad categories of items to transfer that ought to work.

Restore is a great idea but it will fail if you're using more than the target disk's capacity.

Ought to go without saying, but be sure to back up your Mac: Back up your files with Time Machine on Mac - Apple Support

You can use the paid third party app Carbon Copy Cloner (CCC) to make a bootable clone, plus CCC allows you to select & deselect items for copying. It is also a good app for backups as well if Time Machine is not sufficient or if you want a second type of backup.

FYI, do not use Disk Utility to clone anything as it will usually fail (especially for a bootable clone and for larger items). Disk Utility is a terrible app and it just keeps getting worse.

Sometimes using CCC to clone a bootable drive is a good choice while other times performing a clean install of macOS & using Migration Assistant/Setup Assistant to migrate the system as suggested by @John Galt is the better option.

Gerrit Velthuis wrote:

I'm still running Mojave (10.14.6) on my 2017 Retina 5K iMac. This is because every now and then, I have to use some older software (mainly Cinema 4D) which still suits my needs and is pretty costly to upgrade.

But Mojave is getting too old for some other software I use on a daily basis (Photoshop, Safari, Pages Numbers etc.).

A few years ago when I upgraded the main internal volume from Mojave to later macOS, I cleanly installed Mojave and some 32-bit apps to an external volume (Photoshop CS6 13.0.0, Lightroom 6.14, QuickTime Player Pro 7.6.6, QuickTime 6 MPEG-2 Playback Component, MPEG Streamclip 1.9.3b8, JES Deinterlacer etc). I very rarely boot to that anymore, though (my son got frustrated to the 2 minutes it takes to double-boot to Mojave so he coughed up some $$ for new Adobe licenses).

But I guess cleanly installing those old Adobe apps does not work anymore because Adobe's license server does not seem to support them anymore.

→ So it is best to preserve those old Adobe installs, and use CCC to selectively clone them. Or maybe clone all to a large volume, trim it manually, and re-clone to a smaller volume. Or just get another large SSD and clone Mojave to its APFS volume, and use other APFS volumes for other tasks.