Working in oil, watercolor, acrylic, tempera and prints, he was also known for making flutes and as a performing artist who sang, danced and composed music. Nevaquaya received many awards and honors over the years to include Director of Indian Art by the Governor of Oklahoma.

He was chosen Indian of the Year in 1974 at Oscar Rose Junior College in Midwest City. Oklahoma. In 1982 he played the flute at the Night of the First American at the Kennedy Center for the Performing Arts in Washington. DC. In 1986 the Comanche Tribe proclaimed the second Friday in October Joyce "Doc" Tate Nevaquaya Day. Four years later he was designated a Living Legend, Nevaquaya appeared on television over 25 times including "On the Road with Charles Kuralt" and on "Good Morning America".