A native of Wielopole Skrzyńskie (in what was then Austria-Hungary), Kantor graduated from the Kraków Academy in 1939. During the Nazi occupation of Poland, he founded the Independent Theatre, and served as a professor at Kraków’s Academy of Fine Arts and a director of experimental theatre in Kraków from 1942 to 1944. Following the war, he become known for his avant-garde work in stage design including designs for Saint Joan (1956) and Measure for Measure (1956).

Becoming disenfranchised by the avant-garde's increasing institutionalization, in 1955 he and a group of visual artists formed a new theatre, Cricot 2. In the 1960s, he traveled widely with his theatre, becoming known for staging "happenings". His interest was mainly with the absurdists and Polish writer Stanislaw Ignacy Witkiewicz (also known as "Witkacy"). The Cuttlefish (1956) and The Water Hen (1969) were his best known productions during this time. A 1972 performance of The Water Hen was described as "the least-publicised, most talked-about event at the Edinburgh festival".

Dead Class (1970) was the most famous of his theatre pieces of the 1970s. Within the piece, Kantor himself took the role of a teacher who presided over seemingly dead characters who are confronted by mannequins which represented their younger selves. He had began experimenting with the juxtaposition of mannequins and live actors in the 1950s.

His later works of the 80s were very personal reflections. As in Dead Class, he would sometimes represent himself onstage. In the 1990s, his works became well known in the United States due to presentations at Ellen Stewart's La MaMa Experimental Theater Club.

Kantor died in Kraków.