He was a member of the Congress of Deputies in the constituent legislature until 1983, a senator twice and mayor of his hometown Las Palmas de Gran Canaria between 2007 and 2011.

Saavedra was a significant figure in Spanish LGBT history, being the first openly gay politician to hold several high public offices.

Saavedra was born in Las Palmas de Gran Canaria on 3 July 1936 to a middle-class Canarian bourgeois family two weeks before the outbreak of the Spanish Civil War.

[5] Between 1959 and 1962 he studied for a diploma in Business Administration at the Escuela de Organización Industrial in Madrid and at the International School of Comparative Labour Law in Trieste, Italy.

[6] In the summer of that year, Saavedra, together with other jurists and intellectuals, promoted the creation of the Instituto Universitario de la Empresa, an institutional platform to channel the debate on the new economic and fiscal regime of the Canary Islands that was then under discussion.

[5] This institute convened several sectoral meetings and concluded with 64 criteria that laid the foundations for the future Statute of Autonomy of the Canary Islands [es], which would only be possible with the advent of democracy.

[5] Saavedra joined the Spanish Socialist Workers' Party (PSOE) and the Unión General de Trabajadores (UGT) in summer 1972.

[5] In August 1982, the Cortes Generales approved the new Statute of Autonomy of the Canary Islands and Saavadera was elected interim president of the first autonomous government.

[7][8] On 21 June 1985 he resigned after a report in Parliament opposed to the Accession Treaty of Spain to the European Economic Community, referring to the Protocol II on the Canary Islands, which had been signed a few days earlier, was successful.

[5][6][9] Even so, the following 15 July, thanks to the "Progress Pact" signed by the PSC-PSOE, the Communist Party and the nationalist forces, he was again sworn in as president of the Canary Islands.

[7] In 2007, he was elected mayor of Las Palmas de Gran Canaria in a landslide victory, bringing the twelve-year rule of the rival conservative People's Party to an end.

[23][24][25] After coming out, Saavedra joined Miquel Iceta as one of the first openly gay politicians in the history of Spain and he became the first to hold certain high public offices: member of the Cortes Generales, minister, mayor of a provincial capital, and president of an Autonomous Community.