In 1930, after attending classical studies at the Filangieri High School in Vibo Valentia, Calabria, his father Giorgio, a pharmacist, encouraged him to further develop his artistic talent.
He frescoed the chapel of Villa Boimond in Sora (Frosinone) and was awarded at the Regional Exhibition of Calabria.
In 1940, he began teaching at the Academy of Fine Arts in Rome, which did not prevent him from maintaining an active artistic career.
He established himself at Via Margutta 49, a street known for its high concentration of artists, including Guttuso, Franchina, Jarema, Fazzini, Severini, and others.
After the expressionism of his Roman years, he returned from Paris in 1949 with a vision of modern art that none of his friends in Italy could understand.
In 1960, he was invited to teach at the American Art Workshop in Positano (Naples) and to participate in a printing techniques seminar in Milan.
In 1962, the University of Pennsylvania invited him to reorganize the Department of Fine Arts, in collaboration with Piero Dorazio, course director.
Savelli accepted and moved to Pennsylvania, where he lived in Springtown for ten years without abandoning his New York studio.
In 1964, he received the Grand Prix for Graphics at the XXXIII Venice Biennale for twenty-seven embossed white-on-white works.
In 1977, he made a series of forty white-on-white prints and accepted a position as visiting professor at the University of Texas, Arlington.
In 1984, the PAC – Civic Pavilion of Contemporary Art in Milan held a solo exhibition coordinated by Luigi Sansone.
In 1984, he created a remarkable piece dedicated to his wife, Glory of a Broken Wing, to Elisabeth Fischer, extending 1,650 cm in length.
In 1993, he began creating a room in the L'Atelier sul Mare hotel in Castel di Tusa, Sicily, which he could not complete.
On 14 February 1995, the "Luigi Pecci" Museum of Contemporary Art in Prato invited Savelli to create a retrospective exhibition scheduled from June to September of that year.
On 10 March 1995, Savelli left New York and arrived in Milan to personally oversee the realization of both exhibitions.
On 17 April 1995, he felt unwell and was admitted to San Orsola Hospital in Brescia by the Argenterio family, who were hosting him.