Seems to me that if you have a new Mini with only one drive, your -new- drive should fit in there with the old one, no "removal" of the old one is necessary. There is space for -2- drives.
You will need the correct drive-to-motherboard connecting cable.
You wrote:
"I don't need to do a clone of the MAC because it will be new and have no information on it."
Ah, but the -System software- is on the original drive, and you need that to boot the Mac. And, I believe there is other software you will want, such as the "iLife" suite of apps.
You -do- want to save all this stuff. The best way to do that on a brand-new Mac is to "clone it over" to the new drive.
Suggestion:
- get a USB/SATA "docking station" -- they cost only about $20-25
- BEFORE you install the new drive, use the free "CarbonCopyCloner" app to "clone" the contents of the factory internal drive to the new one.
- Once the clone is done, TEST it BEFORE you begin the swap/installation. To do this, restart the Mini, and immediately hold down the Option key and KEEP HOLDING IT DOWN until the Startup Manager appears. Then use the mouse pointer or keyboard arrow keys to select the other drive, then hit the enter/return key.
If your clone is a good one, the Mini should start from the docked drive just as it would as if it were installed inside.
Once you have verified that the new drive is in fact bootable and good, THEN do the swap/installation....