Raised in the town of Corral de Bustos in Córdoba Province, Argentina, Desio began his career in his native country playing for :es:Club Renato Cesarini|Club Renato Cesarini and Independiente, winning the 1993–94 Clausura with the latter. He had departed by the time they claimed the 1994 Supercopa Sudamericana, having transferred to play for Celta de Vigo of Spain's La Liga, whose manager at the time, Carlos Aimar, hailed from the same town. Desio's spell in Galicia outlasted that of Aimar, but in December 1996 he moved to second-tier UD Salamanca where he played only until the end of that season; the team finished as runners-up and were promoted, but Desio would remain at the same level, joining Deportivo Alavés. Earning respect for his combative approach and ball-winning abilities, he immediately helped the Basque club achieve their own promotion as winners of the 1997–98 Segunda División, and alongside a new arrival with a similar style, compatriot Martín Astudillo, played regularly as the side coached by Mané narrowly maintained their status in the top division, qualified for the UEFA Cup and then reached the final of the European competition in successive years – Desio made 12 appearances in the continental run, which included the elimination of Inter Milan, and played the entirety of the 2001 UEFA Cup Final which Alavés lost 5–4 to Liverpool. Having missed only 10 league matches in the previous four years, he was absent for almost all of the following campaign with a serious injury to his right knee sustained in a pre-season match in England, and though he made a successful return to the squad in 2002–03, his involvement was interrupted by two red cards. He retired at the end of that season, aged 33, as the team were relegated. With his spell in Europe lasting nine years, he also acquired Spanish nationality. After retiring as a player, in 2009 Desio became co-ordinator of youth football with his hometown team, Sporting Club de Corral de Bustos, moving on to a similar role at professional club Estudiantes de La Plata in 2013, and in 2017 taking up a post overseeing the underage national squads for the Argentine Football Association, also in collaboration with Verón.
