Tamakehu, who made headlines in 2018 when he took an ambulance on a 14km joyride causing more than $16,000 of damage to the vehicle, was living in a backpackers on December 4 last year.
The defendant's roommates were lying on their beds and a cat called Heidi was "roaming around the room", the court heard.
Tamakehu picked up the pet and hit it, sending it into a bunk bed "with considerable force".
He then grabbed the cat again and this time threw it across the room into a solid metal locker.
Heidi died on the floor.
Judge Smith called it "extreme violence".
A woman confronted Tamakehu over the gratuitous violence and he responded by punching her repeatedly in the head and upper body.
"The victim has then dropped to the ground with the defendant still raining punches," court documents said.
Tamakehu fled the address, leaving the woman with a black eye, a cut and bruises to her face.
When police eventually caught up with him, he denied harming the cat and claimed the victim must have fallen out of bed.
The court heard that only weeks earlier, on September 21, Tamakehu went to a Dunedin home and banged on the victim's door, claiming the man owed him $3000.
Fearing the door would be smashed, the man opened it and told the defendant he had no cash.
Tamakehu demanded something else or else he would "punch him over".
The victim handed over a laptop.
When Tamakehu was arrested, police found the item in his bedroom.
Judge Smith noted the defendant was sentenced to a significant prison term in 2006 and suffered a traumatic head injury in 2014.
She accepted that that injury had a huge impact on Tamakehu's life.
"You have real difficulty controlling mood, emotions and behaviour . . . You simply don't exercise judgment as normal people do," said the judge.
But she added: "That doesn't make it any better for your victim and it doesn't make it any better for Heidi."
