The young bass-baritone received his first singing lessons from Sigrid Rennert in Bruck an der Mur. He studied voice with Prof. Karlheinz Hanser and in the Lied class of Prof. Florian Boesch at the University of Music and Performing Arts Vienna. He received further artistic impulses from Ramon Vargas, Robert Holl and Elina Garanca.

On the opera stage he sang Masetto in Don Giovanni at the Stadttheater Baden near Vienna, Marchese in La Traviata at the Festspiele Klosterneuburg, Figaro in Le nozze di Figaro at the Schlosstheater Schönbrunn, Speaker in Mozart's Magic Flute on a tour of the Teatro alla Scala in Shanghai, and Frank in Die Fledermaus at the Deutsche Oper am Rhein in Düsseldorf.

His concert activities include national and international performances such as various recitals, Beethoven's Ninth Symphony in Bangkok and at the Grosses Festspielhaus Salzburg, J.S. Bach's St. John Passion and Handel's Messiah at the Vienna Konzerthaus, Mozart's Requiem in Germany, Mendelssohn's Paulus at the Golden Hall of the Vienna Musikverein, Beethoven’s Christus am Ölberge at the Tiroler Festspiele Erl and other performances in countries such as Italy, Hungary and Poland, as well as two appearances at KS Elina Garanca's open-air concerts "Klassik unter Sternen" and "Klassik in den Alpen" in summer 2019.

As of season 2020/21 season, he has been a permanent member of the ensemble at the Staatstheater am Gärtnerplatz in Munich, where his roles include Speaker in Die Zauberflöte, Masetto and Leporello in Don Giovanni, Don Basilio in Il barbiere di Siviglia, Alidoro in La Cenerentola, Monterone in Rigoletto and Frank in Die Fledermaus.

Alexander Grassauer is a laureate of several international singing competitions. He won first prizes at the 2017 Hariclea Darclée Singing Competition in Romania, the 2017 International Brahms Competition, the 24th Ferruccio Tagliavini Singing Competition, and second prize at the 2022 Hugo Wolf International Competition for Lied Art in Stuttgart. He also won the prize for the best young talent at the 4th International Otto Edelmann Competition in Vienna and the first prize at KS Elina Garanca's Future Voices initiative.