The tarmac spilled across all three lanes and the hard shoulder when the lorry overturned.
Between 10 and 15 vehicles were involved in the crash, between junction three for Bagshot and junction two for the M25 on Monday morning.
Highways Agency officers had to use special equipment to chip the tarmac off the motorway.
Traffic was forced to a standstill at the time of the crash and a five-mile queue of traffic was reported on the M3, tailing back to junction four at Camberley.
A Highways Agency spokesman said: “It cooled quite quickly and had to be physically scraped off using specialist equipment.
“Because of the amount involved, it will have to be done more than once so it will be a reasonably lengthy operation.”
Police, fire crews, the ambulance service and the Highways Agency attended the scene after the 26-tonne Volvo tipper lorry overturned on to a car.
There were no reports of serious injuries, but three men and a woman were taken to Frimley Park Hospital with minor injuries.