I cannot test this, but I think it's worth a try. Without logging into X, switch to a console
[CTRL][ALT]+[F1]. Login, become root, make a directory to store your current home directory, and then modify the account to move the current home directory.
sudo su -
usermod -d /mnt/tmp/$username -m $username
Login again without X. Define your home partition in /etc/fstab.
sudo su -
It might look like this:
/dev/sdb1 /home ext4 defaults 0 2. When correctly defined, mount it, make sure permissions are ok, modify the home directory again, and then move the files from the old home to the new home.
chown -R $username.$username /home/$username
usermod -d /home/$username $username
Login again with X.
sudo mv /mnt/tmp ~
sudo chown -R $username.$username /home/$username/tmp
Does this work as intended?
You can create a new directory, like /users. Mount the disk inside users. Change permissions on /users/$username to match your username, and then change your home directory path with usermod.