The crash happened at about 0520 GMT and the road was closed for several hours.
Arbroath in Angus was left virtually cut off, with all main routes in and out - including the railway line from Edinburgh to Aberdeen - impassable.
Residents in Stonehaven filled pillow cases with sand from the beach to try to protect buildings, after the rivers Cowie and Carron burst their banks on Sunday.
Some streets in the town were evacuated.
David Fleming, chairman of Stonehaven Community Council, said it had been a "horrendous" night but the water was now receding.
He said: "The river Carron flowed into the town down two of the main streets and the water in the high street was up to chest height."
Mr Fleming said he never seen anything like it in the town.
About 50 people were evacuated from their homes and many more were forced to move to the upper storeys of their properties.
Residents start to clear up in Stonehaven, Aberdeenshire
An Aberdeenshire Council spokesperson said: "Our crews have been working throughout the night providing support to the emergency services, keeping roads clear as best they can and helping with the evacuation of residents.
"The torrential rainfall across a large part of Aberdeenshire has meant that our crews have been stretched very thinly but they have been committed to helping wherever possible.
"Our resources were stretched to the limit. We'd already given out most of our sandbags. Anyone experiencing flood-related difficulties can phone 01224 665470 and we will offer advice, support and assistance."
There were 12 schools closed or partially closed in Aberdeenshire.
Insp Kevin Wallace, of Grampian Police, said the force's focus had moved to the Huntly area, where dozens of houses were affected by high waters from the river Deveron.
He said water had got into a large number of properties on the north side of Huntly.
Dozens of people from a local care home - many elderly and vulnerable - were taken to safety by rescuers after a river burst its banks.
First Minister Alex Salmond, who is the MSP for Gordon, visited Huntly and said: "Many families and elderly people have been affected by what has been the second round of flooding in as many weeks.
"Many people in Huntly and across the north east have had a miserable night and my thoughts are with everyone who has been affected by the flooding."
An Aberdeenshire river bank fishing send ended under water
He thanked council and emergency service staff for their efforts.
Roads have been closed across the Grampian and Tayside regions.
There were three severe flood warnings for parts of the River Isla and River Spey.
Rail passengers on trains from Edinburgh were forced off at Arbroath, where they were advised alternative bus connections could not be organised because of the rain.
Many roads in the same area were impassable, with Tayside Police urging motorists not to drive unless absolutely necessary, and there were landslides in Arbroath and Brechin.
The Met Office said 53mm of rain fell in Aberdeen on Sunday, nearly three-quarters of the usual rainfall for the whole of November.
It fell on ground that was already saturated as the area had seen more than twice as much rainfall as normal for October.
Grampian Fire and Rescue Service said it had experienced its highest demand overnight, with about 350 calls coming in a 12-hour period.
The situation caused serious problems on the roads.
The wet weather caused problems for motorists across Scotland
There are serious problems on the A90 Lang Stracht in Aberdeen. North Anderson Drive was down to one lane northbound between Lang Stracht and Mastrick Rd.
Drivers were forced to abandon their cars outside Arbroath.
A vehicle in Montrose was swept away and Tayside Police reported many drivers were trapped in their cars in deep water.
Moray Council said roads and properties in areas including Rothes and Portessie had been affected by flooding.
The A941 at Rothes was closed following a landslip and 30 stranded motorists spent the night at council centres in Keith.
The SPL match between Dundee United and Rangers had to be abandoned at half-time on Sunday because of the heavy rain.
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