Thanks for your help, William and Mike.
With the Mint Distro, I don't think you can log in as a Root user. I think you can only use the sudo command, in the Terminal, to get Root privileges?
The command line that you suggest, would I have to specify what usb, the portable usb hdd is? ie usb sdc1?
Also, I just remembered about right clicking on the Files slection in the Mint menu, to select Root privileges. I did this and got "elevated" privledges, but I still got the complaint, "cannot copy folder, no permission to read". :-(
So, I remembered about using Puppy Linux and I booted up Puppy from a usb flash drive and had no problem copying the Mint Home folder to the portable usb hdd. :-) Way to go, Puppy Linux. :-)