Acevedo has played for San Lorenzo since 2005, in 2007 he helped the club to win the Clausura tournament. In January 2009, he was signed by FC Metalist Kharkiv but was not important in the team because he did not adapt well to his surroundings in a country that was not his own. On July 3, 2009 Independiente signed the center midfielder on loan from Ukrainian club Metalist Kharkov until December 2009 because of his inability to adapt and his strong desire to return to Argentina. In July 2012, Acevedo was in talks with Colo Colo to play in Chile, but River Plate wanted to retain him for the Apertura.
Acevedo has represented the Argentina national team at Under-17 and under-20 levels. He made his full international debut for the Argentina national team after being called up to join Diego Maradona's squad of Argentina based players who beat Jamaica 2–1 on February 10, 2010.