Jerry Sowood, 27, faced Melbourne Magistrates Court from the police custody cells on Wednesday, a day after he allegedly attacked the young family in the city centre.
Sowood is accused of striking the boy, aged 10, outside Victoria Police headquarters on Spencer Street about 1pm on Tuesday.
After landing a blow to the boy's upper body, Sowood continued walking before doubling back and put the boy's mother in a headlock as she tried to intervene, a witness alleged.
Sowood allegedly used scissors to repeatedly stab the mother, 46, in the upper body before passers-by pulled him off her.
He was charged on Tuesday night with a series of assault-related offences including affray, intentionally causing injury, two counts of unlawful assault, conduct endangering life and conduct endangering serious injury.
Sowood represented himself as he faced court for the first time on Wednesday afternoon.
He told the magistrate he did not want to speak to a lawyer or be assessed by a custody nurse, before discussing the allegations in open court.
"I was in a mental state of mind when I did what I did," he said.
"At least they're both still breathing so I kept my humanity intact."
His video link was muted as magistrate Vincenzo Caltabiano noted there was no application for bail so Sowood would remain in custody until next court date in November.
When Sowood's link was unmuted to confirm he had heard, the 27-year-old then said, "even though I did what I did, a mother did not lose her child".
The boy and his mother, who were visiting from the Phillip Island township of Cowes, were taken to hospital on Tuesday afternoon with non-life-threatening injuries.
The boy's two siblings witnessed the alleged attack.
"Fortunately, they weren't injured," Superintendent Zorka Dunstan told reporters on Tuesday.
"But obviously they have been impacted, witnessing such (an) incident."
Supt Dunstan, who also saw the incident from her office, said police were horrified it could happen outside a police station.
"I'm just grateful that we had people assist immediately," she said.
Police do not believe the parties knew one another.