The statue is a sculpture of a child playing with a butterfly, and police say it appears the statue was cut away from a concrete mount.
The Pingree facility near the University of Utah was founded in 2002 and serves as a school, resource center and research lab for the study and treatment for children with autism.
Valley Mental Health Communications Director Christopher Katis told ABC 4 News that Dennis Smith was commissioned to sculpt the statue in 2002.
The statue is titled "Beyond the Garden" and depicts a boy playing with butterfly on the end of his finger.
Katis said the statue was sawed off at the toes of the boy in the sculpture, and that the tiny butterfly apparently broke off when the statue fell to the ground. Katis said he found the butterfly nearby, which has significance for those who work at the facility.
Katis said teachers and researchers at the Pingree school often refer to the students as their "little butterflies."
Police said no suspects were identified and that the investigation was ongoing.