Prior to his call as a general authority, Stevenson worked as the chief operating officer of ICON Health & Fitness.

[5] He has also served on the Marriott School of Management National Advisory Council and the Utah State University Foundation Board.

During his time in the Seventy, Stevenson served both as a counselor and as president of the church's Asia North Area, based in Tokyo, Japan.

Stevenson was released as presiding bishop six days after he was sustained to the Quorum of the Twelve and was succeeded by Gérald Caussé.

He was sustained to the Quorum of the Twelve along with Ronald A. Rasband and Dale G. Renlund, filling vacancies created by the 2015 deaths of L. Tom Perry, Boyd K. Packer and Richard G. Scott.