When Mr Tate pulled them over down the road from the venue, the Crown alleged he was attacked from behind by the defendant.
Tauatevalu's wife, who was allegedly assaulted by him earlier that night, gave evidence of her husband upper-cutting the officer several times.
Other witnesses who were on the scene shortly afterwards told the court how the man stomped on the officer's head.
In closing, Crown prosecutor Robin McCoubrey told the jury the nature of the attack should push them to arrive at a guilty verdict.
"Walter Tauatevalu's intention went far beyond causing Simon Tate serious harm," he said.
"Leaving the ground to jump on somebody's head, repeated stomping causing the injuries they caused -- he wanted to finish him off."
And he said that would have happened had there not been intervention by a woman.
But defence lawyer Graeme Newell said the evidence given by one witness, who said she tried to thwart the attack and was shoved aside, was inconsistent.
"He may well have been persuaded [to stop] by two women he knew but that doesn't mean he intended to kill," Mr Newell said.
He told the jury to put feelings of sympathy to one side.
"Whether it was a police officer on the ground or a gang member, it shouldn't make any difference," he said.
Mr Newell also highlighted Tauatevalu's explanation that he was pepper-sprayed by Mr Tate, something the lawyer said was backed by the fact his canister was 30mg light when examined.
He said the evidence pointed to his client venting his anger in response to that rather than cold-bloodedly trying to kill Mr Tate.
