Hesayne was the bishop of Viedma for 20 years, until 28 June 1995, when he resigned. He ruled his episcopal see during the dictatorial regime of the National Reorganization Process (1976–1983), and was among the very few members of the Argentine Catholic hierarchy to openly criticize its human rights abuses and crimes, such as the murder (masqueraded as a road accident) of bishop Enrique Angelelli by a military task force in 1976.
Hesayne continued to be a critic of government policies after the return of democracy, especially during the neoliberal rule of Carlos Menem in the 1990s, and his successor Fernando de la Rúa. In 1999 he wrote to Menem after the president called bishop Rafael Rey, president of Argentine Caritas, a liar. Menem had spoken about a decrease in poverty, and Rey had contradicted him, stating that poverty was high and had actually increased over the previous five years. Hesayne told Menem: "You might deceive even the Pope with political fallacies, but not the Lord of the Church and of History, Jesus Christ, for whom what we have truly done for the poor is worth." (Menem had been decorated by Pope John Paul II in 1993 for his anti-abortion stance.)
In 2001 Hesayne again criticized the neoliberal policies of President De la Rúa, and even threatened him with excommunication. In a follow-up letter to him, he told the president: "Is it licit for a Christian to receive the Communion if in fact he assumes the neoliberal ideology that engenders death for millions... death of children just after birth, accelerated death for the elderly and slow death to generations of young ones? [...] All the actions of your government have been in favour of the markets, and against the people."
- Catholic Hierarchy. Bishop Miguel Esteban Hesayne.
- Catholic News Service. 7 August 2006. Argentine church remembers bishop killed during dictatorship.
- (in Spanish) Trial of the Argentine military juntas. 2 August 1985. Testimony of Bishop Hesayne.
- (in Spanish) Umbrales. Interview.
- (in Spanish) Río Negro Online. Interview.
- (in Spanish) Clarín. 12 June 1999. Otro obispo criticó a Menem.
- (in Spanish) Tlahui. Carta de un obispo argentino al Presidente De la Rúa