Born in
Asunción, Paraguay, Cuevas started his career at
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. Cuevas was released by Club América, and trained for brief period with
Premier League club
Portsmouth. Portsmouth and
Blackburn Rovers were strongly linked to him, with the player stating that a move to England was a possibility. However, Cuevas would end up playing the first half of 2008 for
Libertad in his native country and was later signed by Brazilian club
Santos in July 2008. On 15 January 2009, he was released from his contract with Santos. On 9 February, Cuevas signed a six-month deal with
Universidad de Chile, one of the most popular teams in that country. On 7 July, he won the
2009 Apertura tournament with Universidad de Chile ending with 18 match played and 3 goals. At the end of the tournament, he announced that he will not renew with the Chilean club. During the 2009 off-season, Cuevas had trials at
Twente (making his debut in a friendly match played in the Netherlands, which ended in victory against
Borussia Mönchengladbach) and
Hannover 96. Cuevas did not finalize his contract with the aforementioned European clubs and returned to Paraguay to play for
Olimpia Asunción, where he tried to return to the top form he once had during his River Plate years. On 16 December 2010, he signed with Mexican football club
Puebla. On 14 July 2011, Cuevas signed a contract with
Cerro Porteño.
Deportivo Carapeguá Cuevas scored his first goal for Deportivo Carapeguá in a 2–0 home victory against
Club Libertad on 28 August 2012, Cuevas was substituted onto the field in the 69th minute and scored Carapeguá's second goal in the 88th minute. ==International career==