He was named after his father, Spiridon, who was a great shipowner in Trieste, then Austrian Littoral (modern Italy), but had originated from the village of Podi near Herceg Novi, in Boka Kotorska (modern Montenegro), then a part of the Austrian Empire. After the death of his father, when Spiridon was a boy, he was sent to Vienna to be educated. He attended the Theresianum (1861-1865) and Stiftsgymnasium Melk (1865-1869) at Melk in Austria. Following the death of his mother, he became a journalist by trade. He regarded himself first and foremost as a Serb, and that drove him to participate in the 1875 uprising in Herzegovina, and the following year to witness the Montenegrin-Ottoman War (1876-78), and participate in an insurrection in 1882 against the Habsburgs in southern Dalmatia, where he was arrested with Arthur Evans, who was a reporter for the Manchester Guardian at the time. Gopčević worked in these years as a war correspondent in the Balkans, and also travelled to Siberia, North America, North Africa and the Middle East. He even had a chance in London to meet William Gladstone in 1879. Gopčević entered the Serbian foreign service and served as diplomatic attaché in Berlin (1886-1887) and Vienna (1887-1890). In 1891 he went back to his family estate in Trieste, where he continued to write as a journalist for several German-language newspapers.
In 1893 Gopčević spent time in jail due to some of his articles against the Austro-Hungarian government, and decided to end his journalistic career. Astronomy became the dominant interest in Gopčević's life and, to a most unusual extent, his work was his life and his life was his work.
In 1893 he founded an observatory "Manora-Sternwarte" in the town of what is now called Mali Lošinj in present-day Croatia. This observatory was named for his wife, a wealthy Austrian noblewoman. At this observatory, Spiridon used the 17.5 cm refractor telescope at the observatory to make observations of Mars, the rings of Saturn, and other planets. However he would eventually close the observatory in 1909 due to financial problems, and the telescope was offered for sale.
From 1899 until 1908 he was the founder and editor of the Astronomische Rundschau, a popular scientific journal. He spent several years in America before returning to Europe and editing an army journal in Berlin during the war. The circumstances of his death are somewhat uncertain, but he appears to have been impoverished.
In 1889, Gopčević published an ethnographic study titled Old Serbia and Macedonia that was a Serbian nationalist book on Kosovo and Macedonia and contained a pro-Serbian ethnographic map of Macedonia. Gopčević's biographer argues that he did not actually go to Kosovo and thus the study is not based on authentic experiences. Within scholarship Gopčević's study has been noted for its plagiarisms, manipulations and misrepresentations, especially overstressing the Serbian character of Macedonia.  While Gopčević's views on Serbian and Albanian populations in Kosovo and also the issue of the Arnautaš theory or Albanians of alleged Serbian (descent) have only been partially examined by some authors. Noted for being an ardent Serbian nationalist, his book Old Serbia and Macedonia is seen as a work that opened the path for unprecedented Serbian territorial claims in the region.
- Montenegro und die Montenegriner, 1877
- Oberalbanien und seine Liga, 1881
- Bulgarien und Ostrumelien, 1886
- Kriegsgeschichtliche Studien, 2 Bände, 1887
- Makedonien und Alt-Serbien, 1889
- (als Leo Brenner): Beobachtungs-Objekte für Amateur-Astronomen, 1902
- USA. Aus dem Dollarlande; Sitten, Zustände und Einrichtungen der Vereinigten Staaten, 1913
- Das Fürstentum Albanien, seine Vergangenheit, ethnographischen Verhältnisse, politische Lage und Aussichten für die Zukunft, 1914
- Geschichte von Montenegro und Albanien, 1914
- Aus dem Lande der unbegrenzten Heuchelei. Englische Zustände, 1915
- Rußland und Serbien von 1804-1915. Nach Urkunden der Geheimarchive von St. Petersburg und Paris und des Wiener Archivs, 1916
- Amerikas Rolle im Weltkriege, 1917
- Die Wahrheit über Jesus nach den ausgegrabenen Aufzeichnungen seines Jugendfreundes, 1920
- Kulturgeschichtliche Studien, 1920
- Österreichs Untergang : die Folge von Franz Josefs Mißregierung, 1920
- Serbokroatisches Gesprächsbuch verbunden mit kurzer Sprachlehre und Wörterverzeichnis, 1920
- Hodge, Carl Cavanagh (2007). Encyclopedia of the Age of Imperialism, 1800-1914. 2. Greenwood Publishing Group. p. 441. ISBN 9780890968970.
- Brenner, Leo, "postcard" (PDF). p. 57.
- Yosmaolğu, Ipek K. (2010). "Constructing national identity in Ottoman Macedonia". In Zartman, I. William. Understanding life in the borderlands: Boundaries in depth and in motion. University of Georgia Press. p. 168. ISBN 9780820336145.
- Promitzer 2015, pp. 204–205."In 1889 the journalist Spiridon Gopčević (1855-1936) published an allegedly scientific, but for all intents and purposes Serbian nationalist monograph on Macedonia and “Old Serbia” (i.e. Kosovo). Gopčević’s biographer nevertheless argues that the monograph is not the result of authentic experiences and that he was never in Kosovo. While his manipulations with respect the allegedly Serbian character of Macedonia have already been the topic of exhaustive research, his views on the mutual relations between the Serbian and Albanian populations of Kosovo, in particular with respect to the contested notion of so- called Arnautaš” (Albanians of alleged Serbian (descent), have been only addressed superficially by various authors. Whatever the final judgment might be, Gopčević’s monograph represents a singular attempt to combine sympathies for the cultural development of the Serbian nation with the aspirations of Austria-Hungary as a Great Power in the Balkans."
- Elsie, Robert (2012). A biographical Dictionary of Albanian history. IB Tauris. p. 117. ISBN 9781780764313.