Former Middlesbrough footballer Andrews, 21, was told that he made "immature mistakes" as team leader.
"Your career at Middlesbrough was halted and you got taken off the pitch on a stretcher," said Sugar. "This time you're off the pitch in a black cab. You're fired!"
Andrews took 24-year-old Howard Ebison and self-proclaimed "schmoozer" James McQuillan back to the boardroom after his team took a £160.76 loss in a catering challenge.
Yasmina Siadatan lead the girls' team to a £651.43 victory.
McQuillan and Ebison were critical of their team leader's decision to take them back to the boardroom, arguing that Phillip, Majid and Ben should be blamed for a poor sales pitch.
Sugar was critical of McQuillan's waffle and mocked his CV, where he boasts that he "can taste success" when he wakes up in the morning. "What did you have? A curry last night then?" joked the millionaire.
However, Sugar reserved his strongest criticisms for the team leader, whom he said should have understood the task better because of his background in food.
"Where is this expertise of yours? Your shops may do very low cost sandwiches but the principle is there," he said. "You know how much cheese to buy, how much bread to buy, how much butter to buy. A total mess!"
Afterwards, the fired applicant said: "I'm feeling a little bit gutted but I'm going to take it on the chin and make sure that it makes me more determined to get on and make sure I do very well for myself."
The Apprentice continues next Wednesday at 9pm on BBC One.