Schotz was the youngest of six children of Jewish parents, Jacob Schotz, a watchmaker, and Cherna Tischa Abramovitch. He was educated at the Gymnasium, Pärnu, Estonia, then at the Grossherzogliche Technische Hochschule in Darmstadt, Germany.
In 1912, he emigrated to Glasgow, where he gained an engineering diploma from the Royal Technical College. From 1914-1923 he worked in the drawing office of Messrs John Brown, a Clydebank shipbuilders, while attending evening classes in sculpture at the Glasgow School of Art.
Schotz became a full time sculptor in 1923. From this point onwards his reputation grew and he became a full member of the Royal Scottish Academy, head of sculpture at the Glasgow School of Art (a post he held from 1938 until his retirement in 1961), and eventually was appointed the Sculptor in Ordinary for Scotland in 1963. His pupils included the artists Hannah Frank and Inge King (née Neufeld).
He was made a Freeman of the City of Glasgow in 1981. In that same year, he published his autobiography, Bronze In My Blood.
During his career, Schotz produced several hundred portraits and compositions including figure compositions, religious sculptures, semi-abstracts and modelled portraits. His bust of James Maxton is on public display at the Maxton remembrance garden in Barrhead near Paisley. Other publicly-accessible work includes:
These works were all in Glasgow and the surrounding area. He was responsible for the repair on the bridge sculpture at Kelvingrove Park beside the now refurbished art gallery and museum.