Kaufusi was rated by Rivals.com as a four-star recruit and was committed to the Brigham Young University (BYU) to play college football.

[2] After spending two years on a mission for the Church of Jesus Christ of Latter-day Saints in Auckland, New Zealand, Kaufusi played for the first time at BYU in 2012.

[8] He moved back to defensive end his senior year and recorded 64 tackles and 11 sacks.

On January 30, 2016, he attended the Reese's Senior Bowl and was a part of the South's defensive line that dominated and led them to a 27–16 victory.

[13] At the conclusion of the pre-draft process, Kaufusi was projected as a second or third round prospect by the majority of NFL draft experts and scouts.

He was ranked as the ninth best defensive end prospect by NFLDraftScout.com and the tenth best by NFL analyst Mike Mayock.

[19] He competed with Lawrence Guy, Kapron Lewis-Moore and Mario Ojemudia throughout training camp for the backup defensive end position.

Kaufusi competed with Brandon Williams, Carl Davis, Willie Henry throughout training camp for the vacant starting defensive end position left by the departure of Timmy Jernigan via trade.

[23] Head coach John Harbaugh named Kaufusi the backup left defensive end to Brent Urban to begin the regular season.