If your running the version of DietPi v120 or higher. Yep.
Its available in dietpi-software > userdata location: https://dietpi.com/forum/t/dietpi-software-user-data/400/1
Select USB drive to set one up.
Simply run dietpi-software and enter the User data location menu option. Once there, simply select the location you wish to use, or select Manual for a custom location. You can also setup a dedicated USB drive, if one is not currently installed.