Acevedo's parents are of Puerto Rican descent. They were both born in New York City, and lived in Brooklyn where both their sons, Richard and Kirk Acevedo, were born. The Acevedos moved to the Bronx, where Kirk and his brother were raised. Since childhood, Acevedo has shown an interest in acting; he performed before his family in improvised shows. Acevedo was a drama major in high school.
After graduating from LaGuardia High School of Music & Art and Performing Arts, Acevedo enrolled in the SUNY Purchase School of Acting (Purchase College). In the 1990s, Acevedo earned his Bachelor of Fine Arts degree and, as some of his classmates had landed parts shortly after auditioning for Oz, he was also motivated to try out, and subsequently landed the role of the half-crazed gang leader prisoner Miguel Alvarez.
After landing the role of Miguel Alvarez on Oz, Acevedo was promoted to series regular in season two and appeared in the following episodes: 1–26; 34–36 and 41–56. Among his other most notable credits include his roles in Law & Order: Trial by Jury (2005) as Hector Salazar and HBO's Band of Brothers, produced by Steven Spielberg, as Staff sergeant Joe Toye.
He had guest starring roles on well known Television shows such as NYPD Blue and 24. He had a notable recurring role on the Television show The Black Donnellys.
Some of his most well known movies and miniseries he has starred in include The Thin Red Line, Invincible (2006), Boiler Room (2000), Dinner Rush (2000), Arresting Gena (1997) and Kirk and Kerry (1997). He voices Jackie Estacado in The Darkness, the video game adaptation of the comic book.
In 2008, he landed a supporting role on the Fox science fiction horror television series, Fringe as Charlie Francis which he starred on since the show's beginning in 2008. During the show's second season his character began to appear infrequently and was later killed off mid-way into that very same season; he then assumed a recurring status afterward in that season, then he later returned for season 3, before moving onto another show. He played Detective Luisito Calderon on the short-lived U.S. remake of Prime Suspect. Acevedo appeared on The Walking Dead on November 24, 2013.
Since 2015 he has starred in the Syfy television series 12 Monkeys. In August 2017 Acevedo was cast in a recurring role in the sixth season of The CW television series Arrow.
In 1999, Acevedo won an ALMA Award for his role in The 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 Rorschach Group, with Shea Whigham. He was nominated for a total of four ALMA Awards for his role in Oz for the following years 1997, 1998, 2000, and 2001.