It is understood the 41-year-old Oxfordshire man was crushed after the machine overturned, spilling its load onto the roadway.
Shoppers in the town centre heard a loud bang at 9.10am as the vehicle fell over.
Thames Valley Police spokesman Marianne Stockton confirmed that the driver was pronounced dead at the scene.
She said: “We do not have any more information about the man yet, but the Health and Safety Executive have been informed. The investigation is ongoing.”
Work was immediately halted at the £150m shopping complex, set to open in October, and workers at the site were sent home.
A spokesperson for Parkway, Christina Gillings, said: “We can confirm that there has been an accident at Parkway, which has sadly resulted in the fatality of one of our site team.
“Our sincere condolences are with the family at this difficult time and we are assisting the authorities in every way we can.”