Pizzi graduated from the Milan Conservatory in 1884 where he was a pupil of Antonio Bazzini and Amilcare Ponchielli and attended classes with Pietro Mascagni. Shortly after completing his education, he moved to London where he remained for almost 13 years. In 1885 his operetta Lina won the Bonetti Competition. In 1889 his first opera, Guglielmo Ratcliff, won first prize at the Baruzzi Competition. His fourth opera, Gabriella , was commissioned by Adelina Patti and she portrayed the title role when the work premiered in Boston in 1893 at the Metropolitan Theatre with the composer in attendance.
Pizzi returned to Italy in 1897 to succeed Antonio Cagnoni as the maestro di cappella at the Santa Maria Maggiore in Bergamo. He also taught at the Bergamo Conservatory. He returned to London in 1900 where he became a popular composer of vocal pieces. He died in Milan at the age of 79.