Dean Smith has taken falls from galloping horses, engaged in fistfights with Kirk Douglas and George C. Scott, donned red wig and white tights to double Maureen O’Hara, and taught Goldie Hawn how to talk like a Texan.

He’s dangled from a helicopter over the skyscrapers of Manhattan while clutching a damsel in distress, hung upside down from a fake blimp 200 feet over the Orange Bowl, and replicated one of the most famous scenes in movie history by climbing on a thundering team of horses to stop a runaway stagecoach.

Cowboy Stuntman chronicles the life and...