Mario was born in La Habana, Captaincy General of Cuba, in Cuba, when the country was under the sovereignty of the Spanish Empire. They moved to Madrid when he and his brothers were still young. In Madrid, he was part of the Sky Foot-ball club, the first club that existed in the capital, however, in 1900, a conflict between Sky Football members caused some of them to leave (including the Giralts) and create a new club, Madrid Football Club, currently known as Real Madrid CF, with the official creation of the club being held on 6 March 1902 in the back room of Al Capricho, a meeting in which the Giralts were present, and they become members of the first Board of Directors of Madrid FC presided by Juan Padrós.[4]
Following a conflict within the white club that caused the departure of several of its founding members, among whom the Giralt brothers and Antonio Neyra, they refounded Club Español de Madrid, a club founded in 1901, but who had collapsed in the summer.[6] It was in this club where the news of his sports activity was interrupted, suggesting he retired no long after joining Español de Madrid, thus hanging up his boots considerably sooner than his two younger brothers.