In the Mint installer, you will have to use the expert, custom install option, know what you are doing, and know which disk is which, or forget about your attempt, NOW. In the custom install option, there is the option to tell where you want GRUB installed. In this case, you must know what device name and/or partition. If you are not familiar with Linux device names, study up on this first, and on dual-boot with Windows before making the attempt, or else be ready to spend several days (yes I mean days, not just hours) in trouble-shooting where you went wrong.
Again, for emphasis, disconnect your Windows working drive when making this attempt and leave only the optical drive and the external USB drive connected if you don't know what to do in setting up drive partitions, GRUB, MBR and dual-boot. Mint can cope automatically with installing in this configuration, or with a dual-boot with Windows on one drive. Mint can't be expected to cope with a <removable> USB drive as your sometimes Linux boot drive installation. This is a custom installation, there is not going to be nice, neat, fully documented solutions posted on YouTube.