Amuchástegui started his career with Racing de Córdoba, he was an important member of the team that contested the final of the Nacional championship in 1980.
In 1983, he travelled to Spain to join Valencia CF for a fee of US$300,000 but he could not acclimatise to life in Europe and returned to Argentina without signing the contract, Valencia eventually signed Juan Jose Urruti instead, and Amuchástegui spent several months without a club before joining San Lorenzo de Almagro in 1984.
After a successful season with San Lorenzo he joined River Plate where he was part of the championship winning team of 1985–1986.
After a few years in Mexico he returned to Argentina to play for Racing de Córdoba and then General Paz Juniors in the lower leagues.
In 1992, he joined San Lorenzo for pre-season training but walked out of the club without playing a single game for them.