The governor also drew a parallel with another recent raid by al Shabaab militants.
Some 28 people were killed in the area last month when al Shabaab militants hijacked a Nairobi-bound bus, causing widespread anger.
Kenya has suffered a string of gun and grenade attacks since it sent troops into Somalia to fight al Shabaab in late 2011.
“It is sad that we have another 36 people who were attacked and killed late last night in the same manner it happened on a bus recently. It happened at a quarry about 15 km (10 miles) from Mandera town,” Mandera county governor Ali Roba told Reuters by telephone.
A Reuters witness at the scene counted 36 bodies at the Korome quarry. All the victims had been shot in the head, except for four who had been beheaded.
The witness said the workers were attacked while sleeping in their tents at the quarry.