Born in Asunción, Paraguay, Cuevas started his career at Club Atlético Tembetary, a lower division club from Paraguay, before moving to River Plate of Argentina in 1998. He will forever be remembered by River fans for his memorable goals against Racing and Boca, the first resulting in River's championship win. In the 2004–05 season he was transferred to Club América of Mexico, who loaned him out to Pachuca where he was champion in the year 2006. He then returned to Club América.