Sigmund Stiassny was the only son of the Viennese architect Wilhelm Stiassny (1842–1910) and his wife Julia, née Taussig (1848–1916). In 1899 he married Laura Kohnberger and had two children with her, Elisabeth (1901–1986) and Walther Stiassny (1902–1912). The family lived from 1908 at Giselastraße 1 in Vienna's 1st district, where Sigmund also had a gynaecology practice. His father bequeathed his graphic art collection to him, the works being stamped with the inscription "Sammlung Baurat Stiassny". He had already transferred his extensive private library to him before his death. Sigmund served as a regimental doctor during the First World War and lost an eye. After the death of his first wife, he married Else Pollak on 23 June 1918 and had two sons with her, Hans Joachim and Wilhelm Michael Stiassny. After the war, he continued practising as a doctor at his home address, now renamed Bösendorferstraße, where he also kept his collection of around 24,000 graphic art objects and a library of 14,000 books. The planned sale of the collection "in America" in the late 1920s fell through, but in the course of negotiations with the Federal Monuments Authority in 1927 Stiassny donated 190 graphic artworks to the National Library Portrait Collection. Further donations were made in late 1937 and early 1938 (several hundred graphic artworks and magazines).

The last donation was made around a month after the annexation of Austria to the Nazi German Reich, by which time Stiassny and his family were already faced with increasing persecution by the Nazi regime. Because of his economic situation, Stiassny had by mid-July 1938 pawned some of his remaining collection to the Dorotheum in Vienna. Else Stiassny, whom he had divorced in the meantime, managed to flee to France that month with her younger son Wilhelm. Elisabeth, Stiassny's daughter from his first marriage, who had married the paediatrician Otto Gersuny in 1926, fled with her two sons to the USA in 1938. After suffering a stroke, which left him hemiplegic, Sigmund was no longer able to escape. Only his older son Hans Joachim remained with him in Vienna. Under the Fourth Regulation to the Reich Citizenship Act, Stiassny's medical licence was revoked on 30 September 1938, after which he worked as a “Krankenbehandler” (a derogatory designation meaning "treater of the sick") exclusively with Jewish patients. He was forced at the end of 1939 to move with his son to a collective apartment at Nibelungengasse 8/5 in the 1st district. His carer Friedrich Deutsch, also Jewish, helped him to sell objects to finance his living expenses. The confined living conditions no doubt obliged him to sell the remainder of his collection in late 1939/early 1940. Among the purchasers was Rudolf Perlberger, also persecuted as a Jew. Stiassny died on 22 February 1941 in the apartment at Nibelungengasse 8/5 without probate proceedings taking place. His son Hans Joachim and Friedrich Deutsch were both deported in January 1942 to Riga, where they performed forced labour and were subsequently murdered.

The efforts after the war by Stiassny's daughter Elisabeth Gersuny to discover the whereabouts of items from the collection and library through the US Allied Commission for Austria remained unsuccessful. While Stiassny's collection was forgotten, some of its items ended up in public institutions in Austria, such as the Academy of Fine Arts Graphic Collection, the Austrian National Library and the Vienna University Library. Following systematic provenance research in the Academy of Fine Arts Graphic Collection, on 5 November 2021 the Austrian Art Restitution Advisory Board recommended the restitution to Stiassny's legal successors of thirty-three prints donated in the 1980s by the Viennese bookbinder Adolf Schmidt (1900–1986).