After retirement, Pumpido moved into club management. Pumpido began his career at his home city side Unión de Santa Fe. In 1988, he transferred to Spanish club Real Betis where, in 1989, he almost lost a finger during a training session when his wedding ring caught on a nail in the crossbar of the goal.
He returned to Argentina to his first club, Union, in 1991, and played one final season before retiring in 1992.
Although chosen by Argentine coach César Luis Menotti as the third goalkeeper of the Argentine national team in the 1982 World Cup, he did not play in the tournament. Pumpido eventually made his international debut against Paraguay the following year.
He was the starting goalkeeper during Argentina"s victorious 1986 World Cup campaign, playing in all seven games, conceding just five goals in 630 minutes of football, and keeping three clean sheets. Pumpido then broke his leg in the eleventh minute of Argentina"s second game against the Union of the Soviet Socialist Republics. He was replaced by substitute Sergio Goycochea (also his understudy at River Plate), who had not played a game in eight months.
After retiring as a player, Pumpido went into management.
On 23 December 2011, he was hired as coach of the Argentine club Godoy Cruz. On 3 September 2012, he returned Unión de Santa Fe for a second spell as manager.