Lee Pomeroy suffered 18 knife wounds in a “sustained attack” five minutes after boarding a train from Guildford to London in January, the Old Bailey was told.
Darren Pencille, 36, has denied murdering the 51-year-old.
He is accused of first stabbing Mr Pomeroy in the neck after the father accused him of humiliating him in front of his son.
Pencille’s girlfriend Chelsea Mitchell, 27, allegedly picked him up and bought hair clippers and razors for him to change his appearance after Mr Pomeroy’s death.
Mitchell, of Farnham, Surrey, has pleaded not guilty to assisting an offender.
Jake Hallam QC, opening their trial, said the father was killed the day before he was due to celebrate his 52nd birthday.
Mr Pomeroy and his son had boarded a train at London Road station in Guildford bound for London Waterloo at 1:01pm on Friday 4 Janaury.
Mr Hallam told the jury: “He did not leave it alive.
“Within five minutes of boarding that train, Lee Pomeroy had been stabbed in the neck by the first defendant, Darren Pencille.
“It was the first of 18 knife wounds that he inflicted upon him.
“A little over an hour after he boarded the train, and despite the best efforts of the emergency services who rushed to save his life, Lee Pomeroy was dead.”
The events surrounding the killing were captured on CCTV and witnessed by other passengers, the jury was told.
The Pomeroys had got into the same carriage as Pencille and made their way down the aisle, the court heard.
Mr Hallam suggested that the father and son may have been “blocking” Pencille’s way, prompting the response: “Ignorance is bliss.”
Pencille allegedly made the comment twice, prompting Mr Pomeroy to ask what he meant.
Mr Hallam said it led to a row which quickly became “heated”.
He described the row as “fast-moving, unexpected and tragic”.
A passenger has said Pencille was the aggressor, calling Mr Pomeroy a “p***y” and “c***” in front of his teenage son.
Pencille allegedly shouted: “You touch me, you touch me and you see what happens at the next stop.”
Mr Pomeroy was said to have demanded an apology, saying : “You should not have humiliated me in front of my kid.”
Pencille was swearing and accusing Mr Pomeroy of following him up the train, according to another witness.
The suspect called the victim racist, even though he had not said anything racist, according to a woman on the train.
Mr Pomeroy allegedly responded: “I’ve never dealt with someone with special needs before.”
Part of their heated exchange was recorded on a mobile phone.
The defendant allegedly said: “C***, you heard what I said, you f****** heard what I said. Go, put your hand on me.”
Mr Pomeroy replied: “Listen, right. I dare you, I dare you. I dare you. Put your hand on me.
“Put your hand on me ‘cos it won’t end nicely. Put your hand on me!”
Pencille swung the knife and plunged it into his neck seconds later, cutting through the jugular vein, jurors were told.
Mr Hallam said: “Eyewitnesses saw what they thought was the two men trading punches. They were half right.
“They saw Lee Pomeroy punching the first defendant, defending himself, having been stabbed in the neck by him.
“But the first defendant wasn’t punching back, he was stabbing. Again, and again, and again.
“The 18 knife wounds found to Lee Pomeroy’s body when it was examined in a post-mortem provided the dreadful proof of the savagery of the first defendant’s unrelenting assault upon him – with a wound to his neck, eight to his torso, and others to his arm, his hands and his thigh, all inflicted in a matter of seconds in the same sustained attack.”
The trial continues.