I'm assuming you didn't actually install Linux Mint, but just used some program to put the ISO on the USB device? If there is an icon on your desktop to install Linux Mint, this is the case. Note that the ISO is not persistent, and is meant only to test out, install, or repair Linux Mint. If you want to carry Linux Mint on a USB device and be able to add and modify files, you can either look to a program that can make a persistent USB device for you from the ISO, or you can just install Linux Mint to the USB device. To install it, either boot from the ISO on a DVD or USB device, and then install it to another USB device. Make sure also to select to have the GRUB boot loader be installed to the USB device, and not to your primary hard disk (/dev/sda).
Linux Mint 14 Nadia / 64-bit / Cinnamon