Hi gnappi. I had the same problem some time ago. After much trial and error, I found the best way to boot mint externally was from usb hard drive. Too many problems using flash drives. In fact, I am writing this while running mint 13 cinnamon from usb hard drive. If you are interested, here are the instructions:
1. Remove all the hard drives from the machine you are working on.
2. Plug in your usb hard drive
3. Make sure usb booting is enabled in bios
4. Insert Linux Mint DVD in the machine.
5. Turn on machine and boot to Linux Mint DVD
6. When DVD boots up, install Linux Mint as normal
It should detect your usb hard drive and install mint there as it would for a normal sata hard drive. Hope it works for you