While at the marching band he made his first successful song, a polca named Jasy Morotí, in 1918.
The continued beauty of his works throughout the years positioned Giménez as one of the greatest Latin American composers.
Due to the dictatorship of Alfredo Stroessner's government, Giménez went into exile in Argentina.
Giménez compositions ranged from Paraguayan polkas and Guaranias to waltzes and marching songs.
His most famous works include: Añorando a Matto Grosso, Al Papa Wojtyla, Ruperto Bravo, Feliz Cuarto Centenario, Corrientes, Sapukái en las Malvinas, Corasô rasy, Corasô rasy, Panchita Garmendia, Ha che tren, Che valle Pirajumi and Campesina Paraguaya.