Police have arrested a man and woman over an alleged murder at a park in Adelaide's south on Saturday afternoon.

Key points: A 42-year-old man and a 34-year-old woman were arrested at Waterloo Corner

A 42-year-old man and a 34-year-old woman were arrested at Waterloo Corner Police said they intend to charge them with the murder of Hackham West man Shaun Russell

Police said they intend to charge them with the murder of Hackham West man Shaun Russell Police previously said he sustained serious facial injuries in an altercation

Shaun Russell, 36, was found with serious facial injuries near the Corinth Road Playground at Hackham West.

Emergency crews were called just after 3:30pm on Saturday, and Mr Russell was treated by paramedics but died at the scene.

An arrest warrant was issued on Monday for two people wanted in connection with the alleged murder.

A 42-year-old man and a 34-year-old woman, both from Albert Park, were arrested on Tuesday just before 7:00pm.

Police said Major Crime detectives and Star Group officers attended an address at Waterloo Corner in Adelaide's north where the pair was arrested "without incident".

The man and the woman have since been taken to the City Watch House, and police said they intend to charge them with murder.

A blue 2005-model Holden Commodore and a grey caravan were seized from the Waterloo Corner address and will be forensically examined.

SES volunteers searched the playground for evidence after Mr Russell's body was found. ( ABC News: Lincoln Rothall )

Detective Inspector Billy Thompson on Monday said police had found the suspected murder weapon, but did not provide further detail.

He said Mr Russell was beaten to death.

"Mr Russell was a kind-hearted person who would've helped anyone and we believe he came across these two by chance," he said.

Police have previously urged anyone who saw a couple arguing on Honeypot Road, or may have dashcam or other footage, to contact them.