Greater Manchester Police said a 31-year-old man who was arrested on suspicion of the murder of Ryan Lowry, 36, had been detained under the Mental Health Act.
Mr Lowry, from Marple, was chased down the street in Moss Lane, Partington, and attacked by an assailant with an axe shortly before midnight on Thursday, the force said.
In a statement paying tribute to him, Mr Lowry's family asked for donations to a mental health charity to be made in his memory.
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The family said: "It's hard to believe how something like this can happen to someone like Ryan, who did not have a bad bone in his body. All he ever did was to be there, in whatever way he could, for those that needed help.
"As a person full of kindness, strong principles and humour, he will be missed by so many.
"Ryan loved motor cars and motor racing and was co-founder of the Calm All Porsche Trophy series, raising awareness and money for mental health.
"So many people have asked if there is anything they can do at this time. We know Ryan would appreciate, should anyone want to, any donations to Calm."
Detective Chief Inspector Colin Larkin said: "Our thoughts remain with Ryan's family, who continue to be cared for by specialist officers at this dreadful time.
"I would like to reassure the community that, while our inquiries continue, we are not looking for anyone else in relation to this tragic incident.
"The arrested man and Ryan were known to one another and police are working hard to understand the reason for this horrific attack."
Anyone with information can call police on 0161 856 6777, quoting incident number 3649 of 28/02/20, or Crimestoppers on 0800 555 111.