Eugen was one of nine children. In 1892, he began studying under Albrecht Bräuer at the State Academy of Arts and Crafts in Breslau. In 1894 he enrolled at the Academy of Fine Arts in Munich, where he initially studied under Wilhelm von Lindenschmit the Younger and then under Franz von Stuck, who chose Spiro as one of his very first students in 1895. In 1897, Spiro became his master student and was allocated his own studio in the Villa Stuck. From 1899 to 1904 he worked as a portrait painter in his home town of Breslau. Spiro was a member of the Munich Secession from 1900 to 1933, and exhibited numerous paintings in Munich. He went to Berlin in 1904 and joined the Berlin Secession. He then moved to Paris in 1906, where he joined the artists who gathered in the Café du Dôme. It was in Paris that he got to know Hans Purrmann, with whom he remained close friends. Spiro taught at the Académie Moderne and was a co-founder of the Salon d’Automne.
When the First World War broke out, Spiro had to return to Berlin, where he worked as a draughtsman in the Cartographical Institute of the German General Staff until 1917. In 1924 he was elected chairman of the Association of Berlin Artists. He regularly took part in the large-scale art exhibitions in Berlin. In the Berlin of the “roaring 20s”, Spiro enjoyed the high point of his career. From 1933 onwards, Spiro was subjected to anti-Semitic attacks, was forbidden from exercising his profession and had to give up all his official positions. In 1935, he emigrated to Paris, where he co-founded the Union des Artistes Allemands Libres in 1936, which he then presided over in 1938 and 1939. After the German invasion of France in 1940, Spiro fled to Lisbon. In 1941 Spiro and his family were granted entry Visas for the USA. In 1949, Spiro began teaching portrait painting. The Gurlitt Gallery was the first to exhibit Spiro again in Germany, in 1959.