Akash pleaded guilty to murder just months after the stabbing but the conviction was overturned by the Court of Appeal in 2020 so that a jury could determine the insanity issue.
In his repeated opening statement, Crown prosecutor Gareth Kayes pointed out that the burden is on the defence to prove it was "more likely than not" that Akash didn't understand what he was doing was wrong.
"While the Crown does not need to prove motive, if you are looking for one the Crown says anger and jealousy would both be strong contenders," Kayes said, suggesting that the two were in the midst of an argument and Kaur had just said her unborn baby wasn't his when the attack occurred.
"While he was suffering schizophrenia at the time, he knew the killing was morally wrong."
Kaur was believed to be between seven and 10 weeks pregnant when she suffered 18 cutting wounds and 12 stab wounds, including a 10cm gash to her neck and deep punctures to her abdomen and chest. Her body was then dumped at a remote location in Manurewa.
Akash gave multiple explanations to police in the days following Kaur's death. Jurors will have to "untangle" how much of that was due to his paranoid schizophrenia, his lawyer said.
Kincade said Akash thought he was being monitored and followed by strangers who wished to hurt him, and he thought that Kaur was using hand signals to communicate with the strangers in the moments before she was killed.
So far, jurors have heard from only one witness - Detective Victoria Crichton, who spent much of Wednesday afternoon reading aloud text messages between Akash and Kaur in the weeks before Kaur's death.
The texts, many of which were translated from Punjabi, suggested a volatile relationship fraught with allegations of infidelity. But the pair also frequently used terms of affection for each other and professed their love.
Testimony is set to resume on Thursday.