The default docker data folder is /var/lib/docker. This can be changed to another folder with the following steps. These all need to executed as root or with sudo.
Stop Docker on your computer
service docker stop
Create a new docker daemon config
nano /etc/docker/daemon.json
Add the following text and replace /mnt/docker with the path you want to use as the docker data folder
{
"data-root": "/mnt/docker"
}
Save your changes and close the file.
(Optional) If you want to move the existing data to the new folder
cp -rp /var/lib/docker/* "/mnt/docker/"
Start Docker
service docker start
Remove the old folder if everything is working
rm -rf /var/lib/docker