Miniussi 1984 professional tennis player and won the following year in Buenos Aires together with Martín Jaite first time a doubles tournament on the ATP World Tour. Overall, he was able to win five doubles titles during his career, five more times he stood in a double finals. In 1991 he won in São Paulo, his only individual title on the ATP World Tour. Its highest listing in the tennis world ranking he reached in 1992 with position 57 in the singles and in 1988 with position 37 in doubles.
His best individual result at a Grand Slam tournament was the second round participation at the French Open in 1991, he also reached there in the same year, in double the knockout stages.
Miniussi played 1986-1992 a single and double eleven appearances for the Argentina Davis Cup team. In the 0-5 quarter-final defeat to Germany in 1991 he was defeated at the side of Javier Frana in double against Eric Jelen and Michael Stich.
Miniussi joined the Summer Olympics in 1996 in singles and doubles for Argentina. While he was eliminated in the first round against Fabrice Santoro, he won the bronze medal at the side of Javier Frana.