The murder came days after social media starlet Qandeel Baloch was strangled to death by her brother who said he was "not embarrassed" to have killed her, reigniting calls for action against the crime.
Hundreds of women are murdered by relatives in the country each year on the pretext of defending what is seen as family honour, but it is unusual for the victim to be a man.
The latest incident happened in the impoverished district of Dera Ghazi Khan on Monday, police said.
Allah Ditta, 24, was stabbed multiple times by a group of five men after they spotted him in the village of the woman he was allegedly having an affair with.
Man axed to death over 'honour' in Sindh's Tando Muhammad Khan district
A local police official said Ditta began the relationship when he was working for the woman's brother-in-law, and that she ran away with him in May but returned home two weeks later after the village council intervened.
Ditta's arms were cut off as were his lips and nose, the official said.
District police chief Ata Muhammad Khan confirmed the incident: "The victim was taken to hospital where he died."
He added it appeared to be an honour killing and that police were now searching for the suspects. The woman was not harmed.
The killing of Qandeel has triggered fresh calls for legislation to amend the criminal code which allows murderers to avoid jail by seeking forgiveness from a victim's relatives -- a convenient means of escape particularly in honour cases.
The phenomenon of honour killings was examined in an Oscar-winning documentary by Sharmeen Obaid-Chinoy called "A Girl in the River: The Price of Forgiveness".
The film was hailed by Prime Minister Nawaz Sharif, who in February vowed to push through anti-honour killing legislation, but no action has been taken since then.
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