Sawyer was a secondary player for the Cardinals when they made the Final Four of the 1959 NCAA tournament but improved to become credited as the primary reason for the team's success during his junior season.

[1][2] Sawyer's height of 6 ft 11 in (2.11 m) led to an intimidating presence, such as when Western Kentucky Hilltoppers head coach Edgar Diddle remarked before a game that Sawyer was "the biggest man I ever saw" and must be "6 feet 13 or 14".

[4] Sawyer was selected in the 1961 NBA draft by the Los Angeles Lakers as the 13th overall pick.

Lakers head coach Fred Schaus considered Sawyer to "be a couple of years away" from playing in the National Basketball Association (NBA) but expected Sawyer to join the team during the following season.

[5] Sawyer began his professional career in the American Basketball League (ABL) with the Hawaii Chiefs during the 1961–62 season.