Miniussi became a professional tennis player in 1984 and won a double tournament on the ATP World Tour for the first time the following year in Buenos Aires with Martín Jaite . In total, he was able to win five double titles in the course of his career, another five times he was in a double-final. In 1991 he won his only individual title on the ATP World Tour in São Paulo . He reached his highest ranking in the tennis world rankings in 1992 with position 57 in singles and in 1988 with position 37 in doubles.
His best individual result in a Grand Slam tournament was participation in the round of 16 at the French Open in 1991, and in the same year he also reached the round of 16 in doubles.
Miniussi competed in singles and doubles for Argentina at the 1996 Summer Olympics . While he was eliminated in the first round against Fabrice Santoro , he won the bronze medal at the side of Javier Frana.