Girardi was born in Graz; his father was the locksmith Andreas Girardi who had migrated to Graz from Cortina d'Ampezzo. Following the early death of his father, Alexander Girardi was raised by his stepfather who put him into a locksmith apprenticeship. Against his stepfather's wishes, he joined the amateur theatre Die Tonhalle, where his acting talent was discovered; this led to an engagement at the Vienna Strampfer-Theater.
In 1874 Girardi moved to the Theater an der Wien, where he continued to work for 22 years. In 1896/97 he worked at the Carltheater and then two years at the Volkstheater in Vienna. He also had guest appearances at other important theatres in Vienna and toured Germany (Berlin, Hamburg, Dresden).
At the beginning of World War I Girardi retired from the stage and returned to Graz. Two months before his death in 1918, he was called to the Burgtheater in Vienna to play the role of Fortunatus Wurzel in Ferdinand Raimunds's Der Bauer als Millionär.
Girardi was unhappily married to Helene Odilon. Odilon had many affairs and had Girardi committed to a mental asylum (based on a certificate by Julius Wagner-Jauregg, who had not seen Girardi). Odilon and Girardi divorced in 1896. The actress Katharina Schratt persuaded Emperor Franz Joseph to release Girardi.
Aged 67, Alexander Girardi died on 20 April 1918 in Vienna. He is buried at the Vienna Zentralfriedhof, grave 33E-9-16.
Girardi's staple stage role was the comic. He worked in the tradition of Ferdinand Raimund and Johann Nestroy, and he made a significant contribution to the popular Vienna operetta. Girardi created the roles of Blasoni in Johann Strauss's Cagliostro in Wien (1875), Andredl in Karl Millöcker's Das verwunschene Schloss (1878), Jan Janicki in Millöcker's Der Bettelstudent (1882), Benozzo in Millöcker's Gasparone (1884), Kálmán Zsupán in Strauss's The Gypsy Baron (1885), Adam in Carl Zeller's Der Vogelhändler (1891), the title role in Edmund Eysler's Bruder Straubinger (1903), and Pali Rácz in Emmerich Kálmán’s Der Zigeunerprimas (1912). He contributed greatly to the Golden Age of Vienna operetta.
Giradi's life was the subject of the 1954 film Der Komödiant von Wien.
The dish Girardirostbraten (Girardi roast beef) is named after him – a beef dish heavily covered with bacon and button mushrooms. His favourite hat style, a straw hat with flat crown and brim (a boater), became popular as the Giradi Hat. The city of Graz and the Vienna Mariahilf district have a Giradigasse (Girardi Lane) and there is a Girardipark in the district Innere Stadt. The Alexander Girardi International Singing Competition in Coburg is named after him.
- Alexander Girardi in Österreichisches Biographisches Lexikon 1815–1950, vol. 1, p. 446 (in German)
- Alexander Girardi in Aeiou Encyclopedia (in German)