Download instaler only

You'll need to create a macOS Mojave bootable installer: How to create a bootable installer for macOS - Apple Support.

You can then setup an external SSD startup disk for macOS: How to Setup and Use an External SSD as y… - Apple Community.

Jack

In theory you should also be able to boot into Internet Recovery Mode using Command + R which in theory should boot to the online installer for the last OS used on that computer (even if the drive is blank). However, sometimes this will only boot to the online installer for the OS which originally shipped from the factory.

How to get old versions of macOS, also ensure you can run Mojave on the Mac. You did not indicate which model year iMac you own so you need to see if Mojave will run on it.