I'm trying to install Mint Linux to a USB stick, but the Mint live CD doesn't fit on a normal CD and I don't have any DVDs available. The Ubuntu live CD does fit on a CD, so I want to use the Ubuntu LiveCD to install Mint. Is that possible?
Depending on the target distro you can execute from a different distro one of the setup tools. The most popular tools are:
I would suggest to use a Debian or Ubuntu network installation CD, boot a basic system and then use
debootstrap to bootstrap Mint from it. I am not too familiar with Mint, but I know of its heritage. And since I have successfully bootstrapped Debian from Debian, Ubuntu from Debian and Ubuntu from Ubuntu (all the same architecture, however), I have no doubt this will work with Mint as well.
After bootstrapping you can even
chroot into the "new" system after bind-mounting
/sys from the "host" and then install GRUB and so on ...