He was born in Montevideo to parents who moved to Buenos Aires when he was four years old, and he eventually adopted Argentine citizenship. His Spanish parents noticed his musical predisposition and tried to encourage it by sending him to violin and piano classes. He abandoned his studies, however, and entered the work force, first in a bookshop, until 1892, and later in the office of the Director of the San Martín Theatre for a period of 15 years.
He began composing tango pieces during this interim. His first success was La morocha, which sold 280,000 copies following its 1905 recording, and was one of the first tango songs known outside Argentina. The wife of noted ParisiantenorJean de Reszke invited Saborido to perform for high society audiences, and Saborido came into demand as a tango dance instructor.
He returned to Buenos Aires following the outbreak of World War I in 1914, and became a public administration employee. He married Urbana Ruiz and settled the residential Villa Devoto section of Buenos Aires (a daughter, Rosario, became the namesake for his last composition). Saborido made a last public appearance as a performer on the radio, in 1932, and he died at his desk at the War Ministry in Buenos Aires, on September 19, 1941.