Aguirre's film career began in the 1940s, appearing in the Westerns of Pedro Infante, and later in Mexican horror films. Years later, she starred in Los Años de Greta, a drama about coming to terms with aging. In television, she played mothers and grandmothers in countless telenovelas, notably Dulce desafío and its sequel Locura de amor, playing Esther in both.
As a voice actress, she dubbed Angela Lansbury in Murder, She Wrote and other productions and Bea Arthur in The Golden Girls. In films, she dubbed Martha Scott in Ben-Hur, Elsa Lanchester (as Katie Nanna) in Mary Poppins, and Piper Laurie in Carrie. In animation, she voiced Perdita in the 1961 film 101 Dalmatians, Widow Tweed in The Fox and the Hound, Quasimodo's mother in The Hunchback of Notre Dame, Mrs. Ladybug in James and the Giant Peach, Lachesis and Hera in Hercules, Gaia in Captain Planet and the Planeteers, and Baylene in Dinosaur.