Here an already aged Cus D'amato demonstrates the same principle in discussing a prospective match up with Joe Frazier with a young Ali. Ali's dropping his hands for the uppercut cost him in the bout with Frazier exactly as D'amato predicted it would:
The reason Ali could do this was partly his reach advantage, but partly because both Frazier and Moore bent over at the waist to avoid punches. This worked well for them the majority of the time, but it also meant that they had to come out of the stoop to counter. You can't advance across the ring with any rapidity while doubled over. What you will notice over and over in the Frazier is constantly advancing, except when he is bending to avoid punches.
Tyson would bend forwards at the waist when appropriate, but he would more often utilize a bending at the waist to the side, or rather a deep slip. With these deep slips he could get to the side of straight punches and underneath hooks. They aren't a particularly natural maneuver and the stories go that Tyson used to practice them up and down the gym while holding a barbell plate.
Where Joe Frazier would bend straight forwards almost every time with his forearms in front of his face, and this made him very susceptible to the best uppercutters, Tyson kept his eyes up, his back straight, and had control over his body even while deep in a crouch or dip.
The main point was that Tyson was more varied in his evasions than Frazier, but more important he could advance upon his target much faster while he was evading punches—where Frazier had to come almost to a dead halt while he bent over at the waist to avoid the blows.