Acevedo is of Puerto Rican origin. His parents were born in New York City, and lived in Brooklyn, where both their sons, Richard and Kirk, were born. Since childhood, he has shown an interest in acting, by perfoming in improvised shows.
In the 1990s, Acevedo earned his Bachelor of Fine Arts degree and started to appear in various TV Series.
- Person of Interest
- Law & Order: Trial by Jury
- Band of Brothers
- Dawn of the Planet of the Apes
- 12 Monkeys