He studied under the guidance of Miguel Pou starting in 1943 and later worked at the Printmaking Workshop of the Institute of Puerto Rican Culture under Lorenzo Homar's direction from 1957 to 1965. Alicea then became a professor of printmaking and drawing at the School of Visual Arts of San Juan.

Throughout his career, José Alicea has received numerous awards for his graphic work, which includes woodcuts, linocuts, silkscreens, and etchings. He has showcased his art in solo and group exhibitions across Puerto Rico, the Caribbean, the United States, Spain, Chile, Russia, Brazil, and other countries. Notably, Alicea was the first Puerto Rican artist to hold a solo exhibition exclusively of prints at the "Ateneo Puertorriqueño" cultural institution in 1963.

In recognition of his artistic achievements, José Alicea was awarded an honorary doctorate in arts from the University of Puerto Rico, Mayagüez Campus, and from the School of Visual Arts of Puerto Rico in 2000. In 2006, he was honored with a retrospective exhibition of his work at the Museum and Center for Humanistic Studies "Dra. Josefina Camacho de la Nuez" at Turabo University in Caguas, Puerto Rico. His artistic style often incorporates literary texts and writings, addressing social and historical themes through figurative expression.