After landing the role of Miguel Alvarez, Acevedo was promoted to series regular in season two of Oz 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 Joseph 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 as the Governors right hand man Mitch Dolgen. From 2015-2017 he played José Ramse on the Syfy television series 12 Monkeys. In 2018 Kirk played Ted Garza in the film Insidious: The Last Key.
He currently stars as Ricardo Diaz aka The Dragon on the hit series The Arrow.