The gruesome scene was discovered by a neighbour who was looking for their cat at about 4pm on Saturday.
After the alarm was raised, officers found the man's head and arms in a different location on the property in Cork, Ireland.
Efforts to identify the man were initially hampered because his head and limbs were missing, but detectives now believe the man was a rough sleeper in his 50s who was last seen alive on Friday, the Irish Mirror reports.
A report by the Irish Times said the man's head and arms had been cut off, but it was unclear whether the man died at Castlegreina House or if he died elsewhere and his body dumped there.
It is believed the body had been there for some time.
The death was being treated as suspicious and a murder probe was expected to be launched after a post-mortem was carried out.
Investigators have been checking with local agencies to find out if any homeless people were reported missing recently.
A Garda spokesperson said in a statement: "The Coroner has been notified and the services of the State Pathologist has been requested.
"A post-mortem will take place at a later date and this will determine the course of the investigation."
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