Three Melbourne men accused of dismembering and dumping a man's body parts in the Maribyrnong River disposed of his head and hands separately in a failed attempt to conceal his identity, a court has heard.

Matthew Brennan, Edward Hill and Constantinos Spaliaras are on trial over the murder of Brendan Bernard, whose distinctive tattoo on his arm found in the river helped police to identify him in February 2015.

The three men pleaded not guilty to murdering Mr Bernard.

They had all used the drug ice together the day before Mr Bernard's death.

Prosecutor Gavin Silbert told the jury the 32-year-old returned home on the day of his violent death to find the trio rifling through his possessions at the unit he shared with Brennan.

"Brennan, Spaliaras and Hill immediately began assaulting the deceased in the front lounge room area," he said.

"The deceased was taken into the kitchen where his face was cut with a black-coloured throat-cutter knife."

It was alleged Mr Bernard was later choked until he passed out and then taken to the bathroom where the men "tortured" him for 45 minutes.

A witness, who cannot be named, was expected to tell the jury Brennan came out and asked her to check if Mr Bernard was breathing.

Mr Silbert told the court she found a rope around his neck and could not find a pulse.

Deodorant used to mask smell in car

It was alleged Mr Bernard's body was left in the bath for a week and was being washed regularly by Brennan to "stop him from smelling."

Spaliaras and Brennan used a knife and saw to cut up the body before the three men used a stolen car to dump parts in the Maribyrnong River, the court was told.

Mr Silbert said the men used Lynx deodorant to cover up the smell in the car as they drove.

"Brennan, Hill and Spaliaras decided the deceased's head and hands couldn't go into the river as they had identifying features," he said.

"They agreed to dispose of them into a bin."

The men were eventually arrested after the prosecution's key witness, who told police she was with the men at the time of the alleged murder and disposal of Mr Bernard's body, came forward with new evidence.

The trial continues.