It sounds as though GRUB (or to be more precise the boot code of GRUB stage 1) had never been installed in the first sector of your external USB drive where it would have overwritten the original MS-DOS MBR.
I suppose you could go with deppsche's suggestion and again try to boot Mint from the GRUB on your internal drive, or you could install GRUB in the first sector of the external drive and boot from there.
If you want to do the latter, you could do that from the Mint live CD.
First, check the files device.map and menu.lst in /boot/grub of your Mint install on the USB drive to make sure they are correct.
device.map should list (hd0) /dev/sda and (hd1) /dev/sdb if your internal drive is a SATA drive, or (hd0) /dev/hda and (hd1) /dev/sda if your internal drive is an ATA drive.
When you boot directly into the external USB drive, the BIOS considers that drive to be the primary boot drive, and accordingly it should be designated (hd0) in GRUB terminology, whereas the internal drive should be (hd1). Therefore, in menu.lst the first stanza should be something like the following (I'm assuming that Mint resides in the first partition of the external drive and that the system device name of the external drive is sdb, if not revise accordingly)
title Linux Mint, kernel 2.6.17-10-generic
kernel /boot/vmlinuz-2.6.17-10-generic root=/dev/sdb1 ro quiet splash
and the other stanzas should be edited similarly, if needed.
Then ascertain which mount point the Mint live CD has assigned to the Mint partition on the external drive (let's suppose it's /media/usbdisk) and accordingly run the following (assuming that the device name of the external drive is sdb)
$ sudo grub-install --root-directory=/media/usbdisk /dev/sdb
That will install the GRUB stage 1 boot code in the MBR of the external drive and make that partition and any others that are listed in the menu.lst accessible and potentially bootable. You may also want to set the boot flag for the Mint partition, using the Gnome Partition Editor (i.e. GParted).
Then make sure the option of booting from a USB HDD is enabled in the BIOS, reboot and hit F12 (or whatever the keycode is on your system for directly booting from a USB HDD). The GRUB menu for the external drive should come up, offering you the option of booting into Mint.