Stephen Shane Greenfield, 42, was on Friday found not guilty of murdering Mr Mullaly, whose body was found under the Denison Bridge in Bathurst, central-western NSW, on September 20, 2015.
The month-long trial was told Mr Mullaly, 68, suffered stab wounds to his chest and arms, including a fatal injury to the heart.
Mr Mullaly was well-known by locals and had long lived under the bridge in a makeshift camp surrounded by river stones.
NSW Police released CCTV vision of Mr Mullaly's final days in a public appeal.
Crown prosecutor Giles Tabuteau told the jury the case against Mr Greenfield partly relied on the evidence of his former girlfriend, who told police he came home that day and banged on the door to be let in.
"He says … 'I've just done something, I've just killed someone'," Mr Tabuteau said during his opening address in the NSW Supreme Court sitting in Bathurst, describing her recollection.
"She lets him in, he says to her, 'You don't need to know more, I need to clean myself'."
He then used bleach to wash his skin and a Rambo-style knife in the bathroom, according to the woman's version, Mr Tabuteau said.
Mr Greenfield's ex-girlfriend also recalled him saying "I went Tony Mokbel on them", in a reference to the Victorian drug kingpin.
Two of Mr Greenfield's acquaintances said he told them an old man would be found dead under a bridge the day before news of Mr Mulally's death was made public.
Mr Greenfield denied making those comments. Police phone intercepts recorded him telling his former partner he didn't do it and that somebody was setting him up.
The jury rejected the crown case, delivering the not guilty verdict after two weeks of deliberations.
The jury also heard detailed evidence about Mr Mullaly's daily habits and his final days.
Four days before he was found dead, Mr Mullaly visited a bakery where he regularly bought a hot pie and coffee and fed crumbs to the birds outside.
He walked outside Piccolo's Cafe on the main street, captured on CCTV that was later released by NSW Police in a bid to find out more about his death.
A supermarket employee coming home from work saw Mr Mullaly with grazes on his face the day before he was found dead, Mr Tabuteau said.
Two locals out walking checked on Mr Mullaly on the morning of September 20 and found him lying in his camp in a foetal position with bloodied tissues or serviettes in his left hand.
Mr Mullaly's death was the subject of an inquest in 2018, which first aired Mr Greenfield's former girlfriend's recollections.
After the verdict, Mr Greenfield's barrister Ian Nash said he would make a costs application with evidence about the conduct of the trial and the "very different" coronial inquiry.
Justice Richard Cavanagh told Mr Greenfield he could leave the dock and was free to go.
"Mr Greenfield, I wish you well. Other than that, I'll adjourn," the judge said.
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