The driver, who had been asked to make a delivery to the Ballycolman estate in Strabane was attacked shortly after midnight on Thursday.
Between five and eight masked men smashed the driver's side door and dragged him out of the car.
They drove the man to a farmyard and forced him to lie spread-eagled on the ground, before punching and kicking him, and then interrogating him.
Controlled explosions
Chief Inspector Nicky Thompson said three controlled explosions were carried out on a car which was later abandoned outside the Fir Trees hotel on the outskirts of Strabane.
"At this stage we believe there may be a republican element involved but at this stage we are not yet sure which organisation it was," he said.
"The car that the controlled explosions were carried out on is the car belonging to the taxi driver.
"It was abandoned at the rear of the Fir Trees sometime around 0400 BST this morning.
The attackers put a hood on the man's head and left him at Ballindrait near Lifford on the border with the Republic of Ireland.
Police also asked anyone with a farm on either side of the border to check whether their yards had been disturbed.