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. 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 FC Twente 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 is trying 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 F.C.. 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
Cuevas represented Paraguay U23 at the 2000 CONMEBOL Men Pre-Olympic Tournament. Cuevas represented Paraguay at the 2002 World Cup, scoring two goals in Paraguay's final group match, a 3–1 win over Slovenia. Without the two goals, South Africa would have progressed to the second round at Paraguay's expense on goal difference. Cuevas was also in the National team in the Germany 2006 World Cup, and scored the second goal in the 2–0 Paraguay victory over Trinidad & Tobago after an assist by teammate Roque Santa Cruz. Despite the win, Paraguay failed to advance to the second round.
Personal life
His mother, Nidia Amarilla, is also his manager, which is a rarity in the football world. He currently is married to Alicia Ramirez and the couple have one son: Enzo Rafeal born in 2008.
Singing career
In 2013, Cuevas became a singer, after retiring from football with knee injuries. While making success with music, Cuevas dreams of a comeback to sport.
