José Luis Damiani won two titles in his career, both of them in doubles. In 1981 he won his first title in Palermo with fellow countryman Diego Pérez , and in the following season he was victorious with Carlos Kirmayr in Cologne . He achieved his best placement in the world rankings in January 1983 with rank 37. In contrast, he remained without a title in the individual, in whose world rankings he achieved his best result in January 1982 with rank 49.
In Grand Slam tournaments, he never got beyond the second round in singles, which he reached in 1979 at Wimbledon and 1981 at Roland Garros . In doubles he was three times in a row at the French Open in the second round from 1981 to 1983.
Damiani played for the Uruguayan Davis Cup team between 1973 and 1986 . He completed 23 singles and 15 doubles games. In singles he won just over half of his games with 12 games, in doubles he was only victorious three times.