The Joker's truck driver was an accomplice of the Joker.
The middle-aged man was wearing a cowboy hat and driving a large truck with the message "Laughter Is The Best Medicine", which was changed to say "Slaughter" instead. When he distracted a traffic cop by honking the horn, the Joker shot the officer dead.
He was probably killed when the Batmobile chased and eventually caused the truck to crash. The Joker, who was in the back of the truck with his thugs, climbed into the front, shoved the driver's limp body out and took the wheel.