He was the son of the journalist Carmen Gracía García-Nájera and his wife Daría Cumplido Sáenz, and had two siblings.
During the Mexican Revolution, he belonged to the Primera Brigada (First Brigade) which marched on Ciudad Juárez to oust Porfirio Díaz from power.
He founded the revolutionary paper El Noroeste and began his studies at the Escuela Nacional de Medicina (currently Faculty of Medicine of the UNAM) in Mexico City.
Gracia García-Cumplido was cofounder of the Neutral White Cross society (Cruz Blanca Neutral), as well as one of the founders of Escuela Constitucionalista Médico Militar, where he was director and professor of clinical and therapeutic surgery, clinic of traumatology and emergency surgery.
Gracia García-Cumplido was married to the pharmacist Guadalupe Martínez Barragán and died in Mexico City.