One of the men published the address and photos of the policeman's house online, while the other "openly insulted" him, the bureau said.
The policeman, surnamed Chen, was seen killing a leashed golden retriever on a sidewalk in front of a dozen onlookers in a video posted online last month.
Surveillance footage from police showed the dog had attacked at least four people.
Lacking a dart gun and unable to trace its owner, Chen and another officer decided to bludgeon the dog to death "to prevent it from hurting more pedestrians", the local Tianxin bureau of Changsha police said on Weibo.
Infuriated dog lovers also directed their anger at Chen's mother, who was harassed at her convenience store, according to the local Xiaoxiang Morning newspaper.
The Tianxin police bureau also received numerous phone calls questioning the officer's behaviour, it said.
"Killing a dog on the street, no matter a good dog or a mad dog, will cause trauma and pain to some Internet users," wrote one concerned commentater on Weibo.
"I support the police in the crackdown of stray dogs, and hope that they devote greater effort in eliminating the mad dogs in public area," wrote another.