Kluza is a graduate of the Academy of Fine Arts in Krakow, where he studied in Zbigniew Pronaszko's studio. In the 1950s, together with such artists as Józef Szajna, Jerzy Panek and Marian Malina, he co-created a modern artistic formation - the MARG Group (Painting, Architecture, Sculpture, Graphics). He was a long-time teacher of painting and drawing, and then the director of the State Secondary School of Fine Arts in Kraków, which was named after him in 2004. His pupils were Bolesław Chromy, Roman Cieślewicz, Ryszard Horowitz, Marian Konieczny, Roman Polański, Franciszek Starowieyski, Jerzy Trela, Józef Wilkoń and many other famous artists. Józef Kluza's work has undergone strong changes over the years, but he has always remained an avant-garde artist. In the 1960s, he created abstract works, especially abstract expressionism and informel. He also painted figuratively, and his paintings referred to the experience of pop art and new figuration. He aspired to the greatest freedom of expression possible, not subject to the rigours of composition. His art had a close connection with existentialism.