The footage below shows the digger driving through a security gate then tearing the machine from the wall.
It happened at a garage outside Dungiven at about 04:30 BST on Sunday.
The cash machine was lifted into a Citroen Berlingo car which had part of its roof cut off. A number of masked men are seen in the footage.
The raid lasted just over four minutes. Afterwards the car was driven away with the cash machine sticking out of the roof.
It is the latest in a series of cash machine thefts on both sides of the Irish border, with the Police Service of Northern Ireland (PSNI) saying it was the eighth such incident in 2019.
The digger was stolen from a building site further down the road before being driven to the garage