I used to have a JD something like that and I mowed on hills, my property is one big hill. The transmission will hold it back to some degree if you let up on the go pedal. Mine would sit pointed downhill and not go anywhere if I had my foot off the pedal. If it rolls with your foot off the peddle and no break applied it's likely something needs adjustment. The brake is not a brake, it is connected to the transmission and it is internal. If you ride the brake lot you'll need to adjust it more often. The brake and HST pedals should be checked and adjusted regularly, I did mine every spring before the start of mowing. There are instructions for how to check and adjust in the owners manual, or there was in mine.
You didn't say if it is new or used.