Detectives found a second kitchen knife with traces of blood on it not far from the spot where Abraham Baez (24) was killed.
Burke is on trial accused of murdering Mr Baez in a drunken rage following a night out in the party resort of Playa de las Americas.
His girlfriend Sara Stuart is accused of bashing the Spaniard's girlfriend around the head with a rock, knocking her unconscious.
On the second day of the Dublin couple's trial, jurors were shown the volcanic rock, about 6ins long and 4ins wide, prosecutors say Ms Stuart used to attack Laura Negrin.
The jury was told Burke and Stuart went wild and lashed out at police who arrested them shortly after Mr Baez collapsed and died from a stab wound to his neck.
Both suspects kicked out a officers as they were restrained, handcuffed and put in police vehicles, it was said.
Stuart was described as "very violent, hysterical and out of her mind" by one of the arresting officers.
Police also found bloodstains in their holiday apartment, near the scene of the tragedy.
Witnesses said Mr Baez stumbled into a hotel with blood pouring from his neck after being stabbed in a major artery.
When police arrived they found him lying on his back, with his Spanish girlfriend, Laura Negrin, at his side with blood-soaked hair.
She was screaming: "Look what they've done to me! They hit me with a stone these sons of bitches!"
Stuart, who had blood on her face, is said to have approached Ms Negrin, saying "Sorry, sorry, sorry".
Burke later arrived at the scene and tried to drag his girlfriend away, the jury was told.
But they were both arrested and driven to a nearby police station.
All four of those involved in the fight had been drinking heavily.
Tests revealed the dead man was almost four times over the drink drive limit.
Burke and Stuart travelled to Tenerife together as a couple but have since split up.
Burke, now 21, denies murdering Mr Baez and claims the Spaniard attacked him.
He admits carrying a knife on the night of the killing, but says he never took it out of his pocket.
Ms Stuart, now 31, denies assaulting Ms Negrin.
The trial at the the Provincial Court in Tenerife's capital Santa Cruz continues.