Can you give more info about what your setup is and what you want to accomplish?
What OS are you using?
What Mac Mini model, and specs?
Are you wanting to use an external HDD or SSD?
I am unsure if you can save a whole user folder to a disk separate to your boot drive, but there are other options.
You can store some app data and files to separate disks.
You can use the external drive as your boot drive.
You could make a Fusion Drive using your internal drive and an external drive.
Give use some more info, because depending on what you currently have, and what you want to do, there are a bunch of potential options for you.