The deceased hasn't been identified yet, police said.
The body parts -- head, hands and legs -- were found wrapped in a bedsheet in Gopalpur village around 6.30 AM by an auto driver, they said.
Later, around 1.30 PM, the chopped torso of the body was found wrapped in a sack near Sanjay Akhada in Majnu Ka Tila, police said.
It is suspected that the man was murdered a couple of days back, they said.
It was around 7 AM that police came to know about the incident after a PCR call was made by the auto driver.
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The police team, after finding the chopped body parts in the morning, started carrying out a search of the area, and later found the chopped torso, he said.
The body parts had started decomposing which means that he was killed a couple of days back, the officer said.
There were clothes on the body and while the face had not been smashed, the back portion of the head bore several injuries, he said.
Police have begun scanning the CCTV footages from the nearby areas to get clues. It is also suspected that the body was drained off all the blood, washed and then dumped, he added.