Why did Paul VI strip József Mindszenty of his archbishopric?

This can be understood in the context of the "Vatican Ostpolitik".

The Vatican made a secret agreement with the Eastern Orthodox not to mention Communism at the Second Vatican Council; indeed, the word "Communism" appears in none of its promulgated documents.

From De Mattei's The Second Vatican Council: An Unwritten Story, pt. 2, § 11c:

Cardinal [Tisserant] confided […] that he had participated in the negotiations with the schismatic Russian Orthodox: “Moscow demanded that no one speak against communism in the council, and Rome agreed,” he said, adding that he thought it “possible to speak against materialism and atheism without mentioning communism; in this way the council, which deals only with religion, could accomplish its mission perfectly.” […] Cardinal Mindszenty had remained the last symbol of ecclesiastical resistance to communism, after the death of Cardinal Alojzije Stepìnac, who had died of poisoning on February 10, 1962.

ibid. pt. 7, §9 "The Vatican Ostpolitik":

One of the most famous victims of the Vatican Ostpolitik was Cardinal József Mindszenty, primate of Hungary and hero of the anti-communist resistance. Mindszenty, who had been a prisoner from 1948 to 1956, took refuge after the Hungarian revolt in the American embassy in Budapest and always remained resolutely opposed to any idea about dialogue or negotiations with communist governments, convinced that that could only strengthen them. He steadfastly disputed the Vatican Ostpolitik, telling the Secretary of State, Cardinal Villot: “Why do you appoint bishops in the countries of the Eastern bloc? It would be better if there were none, rather than those whom the governments allow you to appoint.”¹⁶² On November 1, 1973, when Paul VI asked him to renounce his title of archbishop of Esztergom and primate of Hungary, the cardinal replied with a respectful but clear refusal. Paul VI took it upon himself to declare the primatial archdiocese vacant, informing Cardinal Mindszenty on November 18, 1973, of his dismissal as archbishop.¹⁶³

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162. ^{A. Wenger, Le cardinal Villot, op. cit., 260.}

163. ^{The announcement of the removal of Cardinal Mindszenty was made in L’Osservatore Romano. According to the Giornale d’Italia dated February 6–7, 1974, the Vatican had “offered his head on a silver platter to his Herod, the communist government of Budapest.” The February 13 issue of the Zürich newspaper Die Weltwoche wrote that now Rome itself was the one to martyr Mindszenty, since it was worried about getting rid of its anachronistic image for the sake of the Vatican’s new Ostpolitik. On February 5, 1974, when the news of his dismissal had become common knowledge, Cardinal Mindszenty issued a communiqué in which he declared that he had never resigned from his post as archbishop nor from his rank as primate of Hungary, underscoring that “the decision was made solely by the Holy See” (Memorie, op. cit., 372).}

Peter Hargitai: The Vatican made a deal with Janos Kadar, the Hungarian communist premiere: Kadar insisted that he would allow Mindszenty to leave Hungary providing his voice remain miuted in exile; when Mindszenty was about to publish his memoirs, Pope Paul VI acted by stripping the archbishop and Prince Primate of his office -- even though he had been tortured by both the Nazis and the communists for not doing their bidding. In a single stroke, the Pope accomplished what the enemies of Christianity could not -- to strip Mindszenty of his office. In the same year, Pope Paul VI receiced the communist dictator Janos Kadar. If this is Vatican "Ostpolitic," it is neither diplomatic nor Christian. I was nine years old during the 1956 Hungarian Revolution and heard a recently freed Mindszenty address his people on the radio. He sounded non-judgmental, humble and to me Christlike. As a Hungarian and a Catholic, I was deeply hurt by the Vatican's action. I can only imagine what that tortured soul must have felt. "Abba, Abba, lama sabbachtani."