In 1958, he received the first scholarship from the Navajo Tribal Council to study outside of the United States, and enrolled in the art program at Mexico City College. There he learned of and was influenced by the work of Diego Rivera. He later studied art at San Francisco State University, where he also worked as a model.

Gorman moved from California to New Mexico, opening the Navajo Gallery in Taos in 1968. It was the first Native American-owned art gallery.

In 1973, he was the only living artist whose work was shown in the “Masterworks of the American Indian” show held at Metropolitan Museum in New York City. One of his pieces was selected for the cover of the exhibit’s catalog.

In 1998, he donated art for Tom Udall’s campaign for election to the U.S. House of Representatives. On April 1, 2003, Gorman donated his personal library to Diné College at the request of the college’s president, Cassandra Manuelito-Kerkvliet.

On September 18, 2005, Gorman fell at his home and was taken to Holy Cross Hospital in Taos. On September 26, he was transferred to University of New Mexico Hospital (in Albuquerque). He died at age 74 on November 3. New Mexico governor Bill Richardson ordered flags flown at half-staff in his honor.