The video of the incident showed the men beating and stripping Wasim Ahmad Tantray before placing him on a pile of hay. They then try to burn him alive.
Police say the video helped them identify the accused.
"We have arrested 12 accused on the basis of the video. At least 15 more involved in the gruesome incident will be arrested soon," said senior superintendent of police Harmeet Singh.
Wasim continues to be in a critical condition.
More than 70 people have been attacked by vigilante mobs this month over suspicion of being "braid choppers" in Jammu and Kashmir.
On Thursday, an angry mob tried to drown a man in the state's famous Dal Lake as they suspected him to be a braid chopper at Hazratbal in Srinagar.
About 200 braid chopping incidents have been reported in Kashmir in the past one month. The police are still clueless about those behind these incidents. A reward of Rs 6 lakh announced by the police gave credence to rumours that an organised group may be behind the braid-chopping incidents.