An English composer of Corsican origin, Mazzinghi was the eldest son of Tommaso Mazzinghi, a London wine merchant and violinist. Apparently at the instigation of both his father and aunt, Mazzinghi commenced lessons with J. C. Bach. He was appointed organist at the Portuguese Chapel in 1775 when only ten years old. He later studied with Sacchini, Anfossi and possibly Bertolini. In 1779 Mazzinghi was apprenticed as copyist and musical assistant to Leopoldo De Michele, chief music copyist at the King's Theatre. Five years later he advanced to the position of harpsichordist and was then engaged as house composer to the King's Theatre (1786-1789). In this position he provided ballet music, directed operas and was responsible for arranging pasticcios. Mazzinghi was a prolific composer for the ballet, having written some two dozen works for the King's Theatre and Pantheon.

Mazzinghi was required to arrange existing music for the ballet as well as compose new works. Among Mazzinghi's more successful ballets were those he composed for Noverre during the period 1787-1789. Paul et Virginie was among the more popular ballets after Noverre's departure for France in 1789. Mazzinghi joined the Royal Society of Musicians on 3 June 1787. He may have had a financial interest in the music publishing firm of Goulding, who published most of his music from about 1792. Mazzinghi died on a visit to his son at Downside College, and was buried in the vault of Chelsea Catholic Chapel on 25 January 1844.