The 22-year-old - whose later rampage through Sydney's CBD was thwarted by a gaggle of good Samaritans armed with a milk crate, a chair and a crowbar - held his phone at arm's length, put his bloodied left hand near his face and then turned the camera to show his victim's body.

"I'm f***ing psycho," he wrote after sending an acquaintance the short clip.

"I was laughing bro. The fear."

Ney on Tuesday pleaded guilty to murdering Michaela Dunn, 24, minutes after entering a Clarence Street apartment on August 13, 2019.

He also admitted stabbing Linda Bo in the shoulder outside the Hotel CBD on York St, as he ran around the city's streets brandishing a bloody 20-centimetre knife and shouted "Allah Akbar" repeatedly.

Agreed facts, tendered to Sydney's Central Local Court, tell of Ney's erratic behaviour in three weeks before the rampage, including his expression of interest in Islam and later decision to stop going to a mosque as "he didn't like the people", and his escape from a secure room in Blacktown Hospital on August 7 during an involuntary admission.

The case will now head to the NSW Supreme Court, which will need to resolve a series of disputed facts, including an allegation that Ney told a person on Snapchat he was "going on terror attack in large shop" (sic).

An extended history of Ney, including his relationship with his father, is also in contest.

Ms Dunn, who met Ney after he agreed to pay $250 for a "girlfriend experience", suffered serious and extensive injuries including a deep wound to her neck and defensive wounds to her forearms and hands.

After killing her in the front room of the unit, Ney filmed his video and placed a murder weapon on the kitchen bench.

He departed down fire stairs, dropping another bloodied knife on the way, and began his frenzied assault on Sydney.

Sprinting down York St, Ney attempted to stab a woman before plunging a knife into the back of Ms Bo's shoulder.

The wound required six stitches.

Pursued by passing firefighters and a man armed with a crowbar, Ney ran through stationary traffic as he yelled "shoot me" and "I'm going to kill you or you kill me".

The then-20-year-old was eventually stopped in Wynyard Lane when another of the men chasing, Jamie Ingham, used a chair to knock the assailant to the ground and then pin him.

Jason Shore then placed a milk crate over Ney's head as a third man struck him in the legs.

In a later police interview, Ney said he couldn't recall stabbing either woman.

When questioning turned to his beliefs, he said: "Yep, I hate the government".

Ney also pleaded guilty on Tuesday to the common assault of his sister, who he struck in the face and placed in a headlock after he escaped from hospital.

He was remanded in custody ahead of a Supreme Court mention on December 11.

Australian Associated Press