He was born in Tempio Pausania, Sassari in Sardinia, to Pietro Angelo Menzio, a high school teacher, and Augusta Pic, both originally from Piedmont.
He served in the Army in the Infantry Battalion during the first World War, among the last young men drafted in combat, the so-called "Ragazzi del '99" ("The boys from 1899").
In 1921, he participated in an exhibition held at the Mole Antonelliana, organized against the more conservative show of the "Societá Promotrice delle Belle Arti" on display yearly at the Parco del Valentino.
In 1926 he was invited for the first time to show in the Venice Biennale and soon after at the First "Mostra del Novecento" and at the "Esposizione delle vedute di Torino" ("The Exhibition of Landscapes of Turin").
During this period, he cultivated relationships with individuals such as Edoardo Persico; Lionello and Adolfo Venturi; Piero Gobetti (who would die soon after) and his wife Ada Prospero; Mario Soldati; Alfredo Casella; Roberto Longhi; and Riccardo Gualino (who would help the painter economically until the advent of fascism).
Thanks to Riccardo Gualino who sponsored the "Teatro di Torino" and Gigi Chessa who designed sets, Menzio got to know foreign artists such as Igor Stravinsky, Sergei Diaghilev and members of the Habima Theater that expanded his vision above the marginality of the Italian art of those years.
In 1929 Menzio resolved to break with the traditional poetics and together with Jessie Boswell, Gigi Chessa, Nicola Galante, Carlo Levi and Enrico Paulucci, they founded the "Gruppo dei Sei" ("Group of the Six") looking for an intellectual freedom and independence criticizing the rising fascist ideology.
After the showcase at the Venice Biennale in 1930, in which Menzio was personally attacked by the fascist establishment, and following a series of international exhibitions at Bloomsbury Gallery in London in 1930, at the Galerie Jeune Europe in Paris and at the Quadriennale in Rome in 1931, the Gruppo dei Sei was dissolved.
Other works such as "Nudo Rosa" or "Figura (con cappello)" (1929; now in private collections, Turin) or "Corridore podista" (1930) show the influence of Henri Matisse and Amedeo Modigliani.