I recommend against that plan. The problem is that, if you're booting in EFI mode, the firmware keeps track of boot options in NVRAM entries. When you disconnect one drive and boot the computer, some EFI implementations notice that the NVRAM contains invalid entries and "helpfully" removes them. Thus, the act of disconnecting one disk after installing an OS on it will make that OS unbootable, at least until you restore the NVRAM entries from a boot of another disk or install a boot manager that auto-detects boot loaders or maintains its own list in some other way.
Instead, just plug both disks in, install Windows, and then install Mint. Ideally, this will work correctly the first time just as it would on a BIOS-based computer. Unfortunately, this ideal isn't always met. There are a number of potential pitfalls that can make things go wrong. The most important of these is the boot mode. Most modern EFI PCs support booting in EFI mode or
in BIOS mode. The trouble is that installing Windows in one mode and Linux in the other mode will create headaches, so it's important that you install them both in the same mode. I'm not sure which mode Windows is using during installation, but you can tell which mode it did use after the fact by examining the partition table. If it's an MBR partition table, the install is in BIOS mode; if the disk uses GPT, Windows was installed in EFI mode. You should then be sure that Linux uses the same mode when you install it. This you can check by dropping to a shell and looking for a directory called /sys/firmware/efi. If that directory is present, then Linux is booted in EFI mode; if it's not present, then you've probably booted in BIOS mode. You can read more on this topic here.
The boot mode of the installer is controlled by firmware policy and settings. Unfortunately, the user-accessible settings vary greatly from one computer to another, so I can't tell you precisely how to force an installation disc to boot in BIOS mode vs. EFI mode. If you want to select one mode or the other, you'll just have to check out your firmware settings yourself.
You can use either BIOS mode or EFI mode; either will work. If you're comfortable with BIOS boot loaders, you might want to favor BIOS mode. EFI mode offers some advantages over BIOS mode, but they're pretty minor right now. (They may become more significant in the future, though.) The biggest advantage right now is that many of the newest EFIs have a "fast boot" mode that can shave a few seconds off the boot time. Another advantage is that it's easier to set up and maintain multiple boot managers or boot loaders, which can be useful if you want to experiment with this class of software.