The gang have targeted traditional Yorkshire flagstones on streets in Roundhay, Moortown and Oakwood.
On one occasion, a group of men were filmed threatening onlooker Tony Quinn while loading the paving slabs into a van.
The victim was approached by a man wielding a pickaxe on Springwood Road, near Roundhay Park.
More video footage shows a getaway car fleeing the scene with a man clinging to the boot.
Residents claim the thefts have been happening on an almost daily basis, and that large sections of pavement are missing.
Historic paths in the Springwood Road and Lady Wood Road conservation area in Roundhay have now had to be replaced with modern paving by Leeds City Council highways teams.
Roundhay resident Tony Quinn said:
"It's happened before, but in the past six weeks it's become an epidemic. On one occasion a woman walking her grandchildren home from primary school saw them, rang police but was threatened. It's day after day, week after week; just this morning I saw another stretch of pavement missing.
"They threatened me with a pickaxe, and I followed them, but they had three vehicles. The pavement is now a patchwork of filled holes. On one street. it's happened four or five times and there are only a couple of stones left. It's a really awful eyesore - only recently the flags on Lady Wood Road were relaid after a long campaign."
Mr Quinn believes the gang use a Transit van, a 'nondescript' car and a smaller van to cruise the area and identify targets.
"They take under five minutes to remove them, then they're transferred into a larger van. There is value in them - quite a few yards offer prices for stone flags. They must have taken a football pitch's worth by now! In the video I took, one of them is riding on the back of the car to try and cover the number plate."
West Yorkshire Police's Sergeant Ian Micklethwaite, of the Inner North East Partnership Working Area, said:
“Local neighbourhood officers are aware of a series of thefts of York stone paving slabs and are actively following a number of lines of enquiry.
“This includes the investigation of an incident in Roundhay in July where a member of the public disturbed thieves in the process of stealing some stone.
“We recognise the impact that this type of offence has on our communities and have increased our patrols of the areas affected to deter further offences.
“We would encourage people to ring us immediately if they see anything suspicious and to take any vehicle details and suspect descriptions from a safe distance without putting themselves at risk.”