DBAN (Derik's Boot and Nuke) is an excellent disk erasing application, even if it is a little slow. It normally uses a three pass overwrite. Two passes writing random characters and one pass writing all 0s. On a large drive, even on a fast computer it can take 3-5 hours to completely erase the drive.
A good alternative is Active Killdisk. This can do a single pass, all 0s overwrite in 1-2 hours. Versions of both DBAN and Active Killdisk are available in Parted Magic, a disk cleaning and repair OS. Download it here: http://partedmagic.com/doku.php?id=downloads
and transfer the ISO image to either a CD or a flash drive just as you would for any Linux OS.
Actually, if you are going to reuse the drive, I would not suggest using a disk erasing program at all, unless the drive has been used a great deal and you want to clean it up. Using Gparted from the Mint live desktop to create a new partition table and format the drive to any file system you want will effectively give the same results for your purpose in much less time.
Once the drive is clean, you can go directly to the Mint disk and install Mint without using any partitioner to premake partitions or format them. The Mint installer includes a partitioning section so all of the required partitions can be set up either automatically or manually at your discretion.
I have never used a Windows Repair Disk to set partitions for either Windows or Linux so I cannot advise you on how to do this. As a general rule, I do not use Windows utilities to work on Linux installations and I do not use Linux utilities to work on Windows installations (if there are Windows tools available). I do know that Windows does not use any of the common Linux file systems so I would assume that they will not be offered as options on the Windows Repair Disk. This is not a big problem because, unless told not to, most Linux installers will format partitions to either ext3 or ext4 by default.
You can use the Windows repair disk if you want to, but it is really not necessary. All the tools you need are in the Mint ISO you downloaded, or, if you prefer in Parted Magic. If you decide to use the Linux tools and need assistance, just ask.