

Yes, I have 2 computers running off of USB with Mint, with persistence. And I’ve set up that for my father in law and a friend too. You boot with one drive, you insert the other one, you UNMOUNT it, and then you load the installer. Please note though, that the bootloader will be installed into the internal drive instead of the usb one. To go around this problem, would be best to disable the internal drive temporarily during installation (either in the bios, or just remove its cable). Then the installer will be forced to write the bootloader on to the usb stick.
I usually set up the partitions as such: 1 GB of fat32 boot partition with the boot flag set, a 4 GB swap partition, and the rest / (root).
These are the instructions at the mint forum.