The 16-year-old opera, horse-riding and theatre fanatic was the fall guy for the boys' team after they came up short in a clothes recycling challenge.
Max was joined in the final boardroom by project manager Patrick McDowell and David Odhiambo, but Sugar claimed that based on "instinct" he had to let the Kent student go.
The boys' team Odyssey were walloped by the girls' team Platinum in the final results, losing by over £120 when the final profits were revealed.
Max was blamed for his lack of sales on the task; however, he insisted that he was too busy organising the sub-team and folding clothes to sell their products.
Coming to his final conclusion on the firing, Sugar said: "When I make my mind up, I have to take into account who I feel has the ongoing potential to go through the process and possibly end up to be the winner.
"Patrick - you totally went off the rails here, I'm afraid to say. You forgot this was a business task. There's no question of a doubt that a couple of the decisions you made were the downfall of this task.
"Max - you're exceptionally great on paper, whether there's any business nous there, I don't know. David - I've got a big concern that you are somebody who causes a bit of friction, you've gone quite close to winding me up a little bit.
"So it's very difficult for me, but I regret that my instinct is telling me that Max - I think you're meant for different types of things. Max - you're fired."
Speaking afterwards, Max said that he hoped his business life wasn't over, commenting: "I do have a passion for business and I am just going to keep on going."
Young Apprentice continues next Thursday on BBC One.