Besides his work in the field of medicine, he had a long militancy in the Colorado Party, political movement that supported the government of the general Alfredo Stroessner who had assumed as president in 1954.
The constants denunciation of Human Rights violation Goiburú made against the government of Stroessner led him to be a part of the group of Colorado Leaders that in 1959 was forced to leave the country in exile.
He was fishing in the Paraná River with his eleven – years old son Rolando, and a few construction workers, when he was interrupt by a military boat with naval Paraguayans officers.
Convinced that the only way Stroessner would leave the government was through violence, in 1974, Goiburú gathered a group of activist of the MOPOCO and a few Paraguayans students from the University of La Plata to plan the assassination of the dictator.
The operative failed several times because of various motives and finally was found out by the police thanks to a navy officer called Evasio Benítez that had been contacted by one of the involved to buy some explosives.
In the year 2006, the Interamerican Court of Justice condemned the State of Paraguay for the murder of Agustín Goiburú and its poor attempts to investigate the truth of his death.