Born in 1879 in Livorno, Italy to a wealthy Jewish family, Mieli was raised in Chianciano, a small spa town in Tuscany, to which his family moved in 1880.
In 1904 he obtained a degree in chemistry, followed by six months of study at the University of Leipzig, attending the lectures of the chemist Wilhelm Ostwald. His chemistry career continued, and in 1908 he moved to the Sapienza University of Rome to work with Emanuele Paterno. He subsequently became a university lecturer in chemistry at the University.