Joseph is the son of Joe Latoma of Zuni Pueblo and a member of the Corn and Water Clans. His mother is Margaret Chavez of San Felipe Pueblo, providing his matriarchal link to San Felipe. In addition to silversmithing, he has been making pots for more than thirty years. He spent his first eight years doing research, interviewing elders and learning on his own: experimenting through trial and error.
Because there is little documented historic pottery from San Felipe, Joseph has created his designs based on the memories of Pueblo elders from both San Felipe and Zuni. In 1989 he began experimenting with local clay as he became interested in researching his Pueblo's traditional pottery styles. He is also very interested in reintroducing traditional San Felipe pottery to both the pueblo and a wider public.
Joseph specializes in polychrome ollas, replicating prehistoric artifacts with a hand-coiling technique. He has taught his wife, Nona, and their children, Dustin, Jaylene, Dalon, Janalyn, and Damon, to make pottery. He explains that this is the best way to teach children about their culture and traditions. He does not put just any type of art on the pottery: the design on each piece is determined by the style of the pottery and each design has a story behind it. Joseph says, "I make pottery to keep San Felipe traditions alive. It's important to me that people know that San Felipe pottery exists." Although Joseph and Nona usually work as a team and collaborate on all of his pots, he acknowledges that Nona has become quite a good potter in her own right due to the fact that she is a "perfectionist... paying attention to the details" of pottery work.