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. In 1897 he began to study at a school run by the friars, being admitted to the Order on 6 August 1902. 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 1904-1906. He returned to the Carmelite monastery and was sent to complete his seminary studies, professing his solemn vows on 7 August 1907. He was ordained a Catholic priest on 19 December 1908 by the Patriarch of Venice. He then served as the prior in several monasteries of the Order, until the outbreak of World War I, at which time he served as a military chaplain. After the war Piazza was again sent to serve as the prior of several local monasteries over the subsequent years. In 1922 he was called to Rome to serve as the Secretary to the Prior General of the Order, serving in that position until 1925, when he was elected as the Procurator General of the Order. 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. Piazza was appointed as Patriarch of Venice in December 1935 and formally installed early the next year. He was elevated to cardinal by Pope Pius XI in the consistory of 13 December 1937, with the title of Cardinal Priest of Santa Prisca. As cardinal, Piazza participated in the Papal conclave of 1939 that elected Pope Pius XII. Piazza remained Patriarch of Venice until 1948 at which time he was named by Pope Pius XII as the Secretary of the Sacred Consistorial Congregation. He remained in this capacity until his death. In 1949 his title was changed by the pope to Cardinal Bishop of Sabina e Poggio Mirteto. On June 11, 1951 he consecrated the Venerable Fulton John Sheen a bishop at the Roman basilica of Sts. John and Paul. Piazza died in Rome on 30 November 1957, and was buried in the Church of Santa Teresa.