Beaver was born in Laramie, Wyoming, the son of Dorothy Adell (née Crawford) (1928-2019) and James Norman Beaver (1924–2004), a minister. His father was of English and French heritage; the family name was originally de Beauvoir, and Beaver is a distant cousin of author and philosopher Simone de Beauvoir and Pennsylvania governor General James A. Beaver. Beaver's mother has Cherokee, German, and Scottish ancestry, and is a descendant of three-time U.S. Attorney General John J. Crittenden.Although his parents' families had both long been in Texas, Beaver was born in Laramie, as his father was doing graduate work in accounting at the University of Wyoming. Returning to Texas, Beaver Sr. worked as an accountant and as a minister for the Church of Christ in Fort Worth, Crowley, Dallas, and Grapevine. For most of Beaver's youth, his family lived in Irving, Texas, even while his father preached in surrounding communities. He and his three younger sisters (Denise, Reneé, and Teddlie) all attended Irving High School, where he was a classmate of ZZ Top drummer Frank Beard, but he transferred in his senior year to Fort Worth Christian Academy, from which he graduated in 1968. He also took courses at Fort Worth Christian College. Later, he attended Oklahoma Christian College. Despite having appeared in some elementary school plays, he showed no particular interest in an acting career, but immersed himself in film history and expressed a desire for a career as a writer, publishing a few short stories in his high school anthology.