Kirk's parents immigrated from Puerto Rico and settled in Brooklyn, where Acevedo was born. Later they moved to the Bronx where Kirk was raised and went to school. Since childhood he had shown an interest in acting; he would perform before his family in improvised shows. Acevedo also participated in his high school's drama club.
After graduating from high school, he enrolled in the SUNY Purchase School of Acting (Purchase College). In the 1990's, Kirk Acevedo earned his BFA (Bachelors Degree in Fine Arts) and soon auditioned for Oz. Some of his classmates landed parts in the series and this motivated him to try out for a part. He landed the role of the half-crazed gang leader prisoner "Miguel Alvarez" in Oz. "Miguel" is a serving time and is involved in many of the situations presented. Acevedo participated in the following episodes: 1-26; 34-36 and 41-56. He was nominated for the 1997, 1998, 2000 and 2001 Alma Award for his role in "Oz".
Among the other series that Acevedo has participated in are Law & Order: Trial by Jury (2005) as Det. Hector Salazar; HBO's Band of Brothers, produced by Steven Spielberg, as SSgt. Joseph Toye and NYPD Blue. Some of the movies/mini series that he's been in are: Bait (2000); Boiler Room (2000); Dinner Rush (2000); Arresting Gena (1997) and Kirk and Kerry (1997).
In 1999, Kirk won an ALMA Award for his role in A Thin Red Line. He was nominated in the "Outstanding Featured Actor in a Play" category 1997 for the Drama Desk Award for Tooth of Crime.
He co-founded the theater company, The Rowschach Group, with Shea Wigham.