Pissis was born on April 26, 1852, in Guaymas in the Mexican state of Sonora. His father was Jose Etienne Pissis (1808–1880), a native of France and a physician, who moved his family to San Francisco, California from Guaymas when Pissis was six. His mother was Juana Bazozabel "Jane" de Bustamante (1824–1893), a native of Guaymas.
