Cuevas was born in Mexico City in 1934. By the age of fourteen, he had illustrated numerous periodicals and books and had had his first exhibition in Mexico City. In 1953 Cuevas published La cortina del nopal (The Cactus Curtain), an article
condemning aspects of the Mexican Mural movement and advocating greater artistic freedom. This philosophy inspired the founding in 1960 of the group Nueva Presencia, which he joined for a brief time.
It promoted individual expression and figurative art reflecting the contemporary human condition.
Cuevas’ work was influenced by the graphic art of Goya and Picasso as well as by Posada and Orozco, whose representations of deformed creatures, degraded humanity and prostitutes were of particular thematic interest. Over the years, he has paid homage to his favorite painters as well as writers, such as Dostoevsky, Kafka, Quevedo and Sade, in numerous series of drawings and prints. Cuevas has said that his drawing represents the solitude and isolation of
contemporary man and man’s inability to communicate. It is for this reason that he often distorts and transforms the human figure to the point of uniqueness.
Cuevas has had solo exhibitions in museums and galleries throughout the world including the University of Texas, Austin, 1961, the San Francisco Museum of Art, California,1970, the Museo de Arte Moderno, Mexico City, 1972, Museo de Arte Contemporaneo, Caracas, 1974, Phoenix Art Museum, Arizona, 1975, Musee d’Art Moderne, Paris, 1976. His work was included in Four Masters of Line: Jose Luis Cuevas, Alexander Calder, Stuart Davis, and Morris Graves, Musee de la
Napoule, France, 1957 and in The Emergent Decade, Cornell University and Solomon R. Guggenheim Museum, New York, 1965. Among his many awards are First International Prize for Drawing, Biennial of Sao Paulo, 1959, First Prize, International Black and White Exhibition, Lugano, Switzerland, 1962, First International Prize for Printmaking, Triennial of Graphic Arts, New Delhi, India, 1968, First Prize, III Latin American Print Biennial, San Juan, Puerto Rico, 1977.
Cuevas was awarded the National Prize for Fine Arts in Mexico in 1981 and represented Mexico at the 1982 Venice Biennial. In 1992 the Museo Jose Luis Cuevas was opened in Mexico City