In emotional testimony to the court, Gina Tsalikian, the dead boy's mother, accused Korkoneas of intentionally shooting her son and walking off "as if he had just squashed a cockroach".
She labelled the officers "monsters" for the alleged shooting.
Korkoneas has said that in the December incident he fired in the air to disperse youths, including Grigoropoulos, who threw stones at his police car.
An autopsy report indicated that the boy was hit by a bullet that ricocheted onto him.
But lawyers for the Grigoropoulos family point to the testimony of witnesses who say the policeman took aim and fired.
Greek authorities decided to hold the trial in Amfissa, which is 200km northwest of Athens, after one far-left group threatened to kill Korkoneas.
Greece's supreme court has rejected bids by the teenager's family to move the trial back to the capital.
Tsalikian, who has also appealed to George Papandreou, the Greek prime minister, argues that holding the trial so far from Athens hampers the presence of key witnesses.
Several banks and shops in Amfissa, a town of 12,000 inhabitants, have boarded their storefronts for fear of violence.