Connect the new drive to the Mac > open Disk Utility > select the name of the drive > click on Erase (this will erase anything on the new drive) > name the drive > select Mac OS Extended (Journaled) in Format > select GUID in Scheme > click on Erase and wait until finished. Click on Partition > click on the + sign > select the size of the partition (make the TM partition as big as possible, at least 2-3x the size of the data on the internal drive it's backing up) > name the partition > select Mac OS Extended (Journaled) in Format > click on Apply > click on Partition.
You now have two partitions; each will act like a separate drive. Open TM Preferences and Select Disk (the TM partition). I believe the other partition will automatically be excluded from backup, but if not, click on Options > + > select the second partition (the non-TM partition).
Now you can use the second partition like a separate drive to save to.