Puts was born in St. Louis, Missouri, and grew up in Alma, Michigan He studied composition and piano at the Eastman School of Music and Yale University, earning the Doctor of Musical Arts degree from Eastman. Among his teachers were Samuel Adler, Jacob Druckman, David Lang, Christopher Rouse, Joseph Schwantner, Martin Bresnick, and, in piano, Nelita True. He also studied at the Tanglewood Music Festival with William Bolcom and Bernard Rands.
He is composer-in-residence at the Fort Worth Symphony and has received a commission from the Aspen Music Festival. His Cello Concerto was premiered by Yo-Yo Ma. Puts's works have been performed by the St. Louis Symphony, the Pacific Symphony, the Utah Symphony (with Evelyn Glennie as percussion soloist), the Miró Quartet, and Concertante. He is a frequent composer in residence at the Cabrillo Festival of Contemporary Music, which commissioned his fourth symphony and his flute concerto.