De Galindez was a committed anti-facist who ran afoul of Francisco Franco's regime in his native Spain during the 1930s. In 1939, he emigrated to the Dominican Republic as a refugee. While in the Dominican Republic he became Secretary of the Dominican Minimum Wage Committee and legal adviser to the National Department of Labor, but he was fired after he expressed sympathy for striking works. De Galindez then moved to New York City, where he became one of the most active leaders against Generalissimo Rafael Leonidas Trujillo's dictatorship in the Dominican Republic.

While in New York, de Galindez taught political science and worked towards his Ph.D at Columbia University, and authored The Era of Trujillo, an exposure of the brutality of Trujillo's rule. He feared for his life, as Trujillo's agents had killed other activists on American soil and one of his own friends was killed in Manhattan in 1952. Two days after his friend's murder, de Galindez wrote a letter stating if he were to be murdered or to vanish, Trujillo's agents were almost certainly responsible. He left the letter in his personal files, to be opened in the event of his death or disappearance.

De Galindez was last seen on March 12, 1956. At 9:20 p.m., he finished teaching a class at Hamilton Hall on the Columbia University campus. He accepted a ride from one of his students, who dropped him off at the entrance to the subway at 7th Avenue and 57th Street. De Galindez was last seen walking towards the subway, carrying his briefcase. He was reported missing five days later. All his clothing, personal belongings, money and papers were found in his room. In June 1956, Columbia University awarded de Galindez his Ph.D in absentia.

In 1964, the former warden of the Dominican prison outside Ciudad Trujillo in the Dominican Republic stated de Galindez was abducted by Trujillo's agents, drugged, put aboard a plane and flown to the Dominican Republic. The warden said he was assassinated in the presence of Trujillo himself, and his body was buried in an unmarked grave. The pilot who flew him into the country and the nurse that provided the drugs were later killed because of what they knew. The warden's account has never been confirmed. Trujillo was assassinated in 1961. The Era of Trujillo, which was unpublished at the time of de Galindez's disappearance, was eventually published in Chile and became a bestseller throughout Latin America.

Foul play is suspected in de Galindez's disappearance due to the circumstances involved. No one has ever been charged in his case.