The singer-songwriter Anaïs Mitchell grew up on a sheep farm in semirural Vermont to a soundtrack of folk ballads and protest music. As a child, she believed that “if you could just write a song good enough, you could change the world.”

That belief has never quite left her. She is testing it in her first musical, the theatrically frisky and musically daring “Hadestown,” a version of the Orpheus myth retold in the American vernacular, which just opened at New York Theater Workshop.

Charles Isherwood, writing in The New York Times, complimented her “lovely music and well-turned lyrics.” Variety called the work “spellbinding.”

Now settled in Park Slope, Brooklyn, with her husband and young daughter, Ms. Mitchell, 35, looks like someone who knows her way around incantation and enchantment. With her choppy blond hair and aquamarine eyes, she has a sprite-like, ethereal quality, which can belie her artistic savvy.