Peter O'Ryan was arrested on Tuesday night after police were called about a man suspiciously loitering around Tyers-Walhalla Road, near where the attack happened in the small Gippsland town of Tyers.
O'Ryan was charged with three counts of intentionally causing serious injury, police said.
The 48-year-old refused to leave the cells when his case was called in La Trobe Valley Magistrates Court on Wednesday.
In his absence, the magistrate remanded O'Ryan in custody and noted management issues including paranoid schizophrenia, panic and anxiety disorder, and depression.
The maximum penalty for the charges is 20 years in prison.
O'Ryan was at his family's home in Tyers, in Victoria's east, on Saturday when an argument broke out just after midday, police allege.
He then allegedly attacked his brother with an axe before turning on his elderly parents.
He fled on foot, sparking warnings for the public to stay vigilant.
Detective Senior Sergeant Rodney Findlay described the attack as among the worst he had seen.
"I've been working in family violence a long time," he told reporters on Sunday.
"This is some of the most serious offending I've ever seen."
O'Ryan's father, 77, and brother, 47, were airlifted to hospital with life-threatening injuries and were now in a stable condition.
The pair required immediate surgery and remained in intensive care at The Alfred Hospital.
His mother, 74, was taken to hospital with critical injuries and remained in a stable condition.
She had only been able to provide sparse details in between treatments of what occurred.
"Over the past three days, police conducted numerous searches for the Tyers man who will now be interviewed in relation to the incident," police said in a statement.
"Police thank the public for their assistance in locating the man."
O'Ryan will return to court on January 14.
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