He was born in Vigo di Cadore, a small village in the mountains of the Veneto region of Italy, the son of Giuseppe Piazza and Elisabetta Nicolò.

He professed his religious vows on 7 August 1903, after which he was drafted to fulfill his military obligations by serving in the medical corps in Treviso from 1904 to 1906.

He returned to the Carmelite monastery and was sent to complete his seminary studies, professing his solemn vows on 7 August 1907.

On 29 January 1930, Piazza was appointed as the Archbishop of Benevento, for which office he was consecrated as a bishop the following 24 February in the Discalced Carmelite Church of Santa Teresa, Rome.

On 11 June 1951 he consecrated the Venerable Fulton John Sheen a bishop at the Roman basilica of Sts.