The 45-year-old Mayweather floored his opponent with a right hand as his former welterweight foe Manny Pacquiao watched ringside in Saitama.
The American Mayweather, who retired in 2017 with an unbeaten 50-0 record, dismissed any prospect of a fight with the similarly retired Pacquiao.
Mayweather arrived at Saitama Super Arena, north of Tokyo, just an hour before his bout.
He was shown on TV relaxing in a dressing room full of takeaway fast food, prior to making his ringwalk.
On another easy payday for the self-styled "Money" Mayweather, the bell to end the second round sounded as Asakura hit the canvas, but it failed to save the Japanese fighter and he was unable to beat the count.
"It was another blockbuster turnout... boxing for me is like breathing," Mayweather said, adding he is looking to fight more "YouTubers and MMA guys".
"I retired for a reason," said Mayweather. "I'm here to have fun and enjoy myself... but I'm not going to take no punishment to the point to where I can barely walk and barely talk.
"People will always pay to get a glimpse of Floyd Mayweather," he said, before asking, "so why would I go out there and fight a top fighter when I can get the same amount of money for three rounds with whoever?"
Asakura, an MMA star and popular YouTuber in Japan, gave Mayweather more of a workout than the last time the American fought an exhibition in Japan, against kickboxing prodigy Tenshin Nasukawa in December 2018.
"I'm glad he threw a few shots, got the crowd excited. That's what it's about," Mayweather said.
"I'm proud of him. I'm proud he came out here. He helped me entertain people. He did what he was supposed to do... We both had fun."
The Mayweather-Asakura bout had no judges, meaning the result would not count on the fighter's record.
Mayweather predicted last week that the fight would be an "easy payday, easy cheque, easy opponent".
His retirement has not stopped him from raking in millions of dollars from a series of exhibitions.
In his 2018 match with Nasukawa, a kickboxer less than half his age, Mayweather floored him three times in the first round in a two-minute fight that he hinted online had netted him $9 million.
