The Office of the Medical Investigator will determine the cause of death, he said.
Eight students were taken to Espanola Hospital for treatment. Six were treated and released while two others were transported to University of New Mexico Hospital in Albuquerque, Espanola Hospital spokeswoman Niki Allcorn said.
One student was airlifted to UNM hospital from the scene, Allcorn said.
An 8-year-old suffered a broken back and 16-year-old had a broken jaw, authorities said.
School officials say the students were headed to Ojo Caliente Elementary, Mesa Vista Middle and Mesa Vista High schools from Vallecitos in northern Rio Arriba County.
Images from a KOB-TV helicopter showed the bus lodged in an embankment. It appears to have gone off a cliff around 15 miles from the schools in Ojo Caliente, a resort town known for its hot springs. The roads are surrounded by mesas, sagebrush and rocky terrain.
An investigation of the crash was ongoing by the Rio Arriba Sheriff's Office and New Mexico State Police. Authorities blocked off access to roads leading to the crash site.
The isolated Mesa Vista Consolidated School District is located in El Rito and is around 120 miles north of Albuquerque. It has an enrollment of close to 400 students.