Yes that should work fine.
Format the drive and make a new directory. Then use cp -a /home/tardigrade/* /mnt/home/tardigrade. Then re-name /home/tardigrade /old/home/tardigrade and then edit your /etc/fstab to mount your new /home partition and check that everything is ok. If all is fine delete the old /home.
A useful reference can be found
here .