Sanchez, 40, signed a contract extension in January to remain in charge until the end of next season.
However, Deportivo won just two of their last 22 league games and were beaten 8-0 at home by Barcelona on 20 April as they finished 15th.
Former Spain and Real Madrid midfielder Sanchez was in charge of Deportivo for 13 months.
Deportivo La Coruna have sacked boss Victor Sanchez after a disappointing end to their season in La Liga.