The man, known only as Valerij R, is accused of murdering a 68-year-old man known as Eduard C during a theft at a jewellery shop in Glarus in 2005.
He is also accused of killing another 48-year-old man known as Peter V at another shop in Zurich-Enge in 2005.
Both men were beaten so badly by the trained martial artist that both succumbed to their injuries, online news website Blick reported.
Valerij R is said to have stolen watches worth over 750,000 francs ($809,232) during these and three other robberies from stores in Zurich over a two-year period.
Having admitted to killing Eduard C, he told the court that he had not expected his victims to go quiet after the first blow.
“I did not intend to kill him,” he said of Eduard C., adding: “You should not play the hero and defend your goods.”
Valerij R was arrested in Germany one week after the killing of Peter V. He was found to be carrying a knife and jewellery.
He was linked to the 2005 murder when DNA was matched with that found at the crime scene.
At first he admitted to the murder of Eduard C, but later retracted his confession.
According to psychiatric reports, Valerij R is treatable, although when asked by the court whether he would agree to such treatment, he said that he does not need it.
The prosecution is seeking life imprisonment with further detention, while the defence has requested 12 years for manslaughter. The verdict has yet to be passed.