No problem. That's a common scenario.
I recommend plugging your new HD into the first connector on your board, and unplugging your old drive during installation, but it's not critical.
After you get the new system installed (make sure you do it on the new drive! (-: ), plug in your old drive, boot to the new system, drop into a shell and type
sudo gparted -l
which will list all known hard drives, the manufacturer/model, the size and their respective partitions. You should be able to decipher which is your old drive. Look at the partitions and sizes of the drive. The disk itself has a name such as
/dev/sdb and the partitions are numbered starting at 1. So the first partion on the drive will have a name such as
/dev/sdb1 (partition number 1). Choose which one you want to mount, it will probably be
/dev/sdb1 but could be anything, so look at the output of
sudo gparted -l.
Choose where you want to mount it (usually under
/mnt), make the directory, for example
sudo mkdir /mnt/old
and mount it
sudo mount /dev/sdx1 /mnt/old
where /dev/sdx1 is the partition you identified from
Check it out,
ls /mnt/old etc. and then add a line to
/etc/fstab so that it always mounts when you boot. After that everything on your old drive will be available under
/mnt/old or wherever you put it.
I'd like to mention that this is a great time to experiment with other distros. For example, you could plug in the new drive, and from your existing installation, you can partition the drive, make filesystems, and run
debinstall to bootstrap a new Debian system without any installation media. You will probably have an extra 10 to 50 MB to put some other distros to experiment with. Nothing wrong with mint, but it's somewhat limiting on installation options.
Good luck to you and come back if you have any more questions.