Is there an easy way, given an ISO image for Linux Mint, to install it to an empty hard drive from within my existing Ubuntu installation? I don't have any CDs or appropriate USB devices at hand, so I'm looking for a convenient way to install it without going out and buying some.
It is possible to use GRUB2 to boot from an iso file, although it is elaborate. I myself haven't tried it yet apart from my experiences with wubi (and that is a different beast), but here are two links that should help you get started:
You could accomplish this by setting up a virtual machine (using something like VirtualBox). Set the boot media to the iso file and it will easily boot it up. Also configure the VM to have direct access to your empty hard drive, and use that as the primary drive. You should be able to run the install from inside virtualbox, then shut down, switch to that drive as your primary, and be good to go.
Just be careful you attach the right drive to the VM so you don't wipe your system!
As an alternative to vorbote's mention of using grub to boot to the installer iso file, you could also setup a temporary ~1GB partition and use the tools that create a live-usb disk to copy the iso's files there and mark it as bootable. Then you boot up to that partition as if it was a usb disk, and run your install from there.
Lastly, and the way I would do this with my distro is using a simple boot-strap. Package managers can often be given a batch configuration file and a target to build a new system on. You don't mention what your current system is and I don't know how Mint would handle this.