Cruz was born on November 8, 1958, in the Bronx, New York. She began writing plays when she was only a child, which she produced in the puppet theater that her father built for her. She graduated from high school at the age of sixteen and attended nearby Queens College from 1975 to 1976, initially as a math major. She received her bachelor's degree in fine arts from Lake Erie College in 1980 and her master's degree in fine arts in playwriting from Columbia University in 1984.

From 1985 to 1988, Cruz was a playwright in residence at Latino Chicago Theater Company. She also worked with Maria Irene Fornes's Playwright's Laboratory, a professional workshop in New York specifically for Latino writers. Many of her works developed out of Fornes's workshops.

Cruz was helped early in her career through the Fund for New American Plays Awards, which provided funding to Cruz and the theater that...