Joseph Sanchez was born in 1948 in Trinidad, Colorado. He is of Indigenous descent, tracing his heritage to Taos Pueblo and Mescalero Apache, as well as Spanish and German ancestry. In the late 1960s, Sanchez enlisted in the United States Navy, serving until 1970, when he relocated to Canada. He lived in Manitoba during the early 1970s, where he became involved with local Indigenous artists and community arts initiatives.
While residing in Winnipeg, Sanchez became a founding member of the Professional Native Indian Artists Inc. (PNIAI) in 1973, alongside Daphne Odjig, Norval Morrisseau, Alex Janvier, Jackson Beardy, Eddy Cobiness, and Carl Ray. The collective, informally known as the Indian Group of Seven, organized to advocate for the professional recognition, institutional inclusion, and self-determination of Indigenous artists within the Canadian arts system. As a member of PNIAI, Sanchez contributed paintings and drawings to the collective's collaborative discussions and regional cultural initiatives.
Following his years in Canada, Sanchez returned to the United States, living and working in New Mexico and Arizona. He expanded his practice to include museum curation and cultural administration, with an emphasis on Indigenous and Chicano contemporary art. From 2002 to 2005, he served as the visual arts director and curator at the National Hispanic Cultural Center in Albuquerque, New Mexico.
Sanchez's work received renewed national attention in Canada through the major museum touring retrospective 7: Professional Native Indian Artists Inc., organized by the MacKenzie Art Gallery in Regina, Saskatchewan, in 2013. The exhibition traveled to several public institutions across the country, including the Winnipeg Art Gallery, the McMichael Canadian Art Collection, and the Art Gallery of Alberta. Sanchez lives and works in New Mexico, where he maintains his practice in painting and independent curatorial projects.