The young bass-baritone received his first singing lessons with Sigrid Rennert in Bruck an der Mur. He then studied singing 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 Elīna Garanča.

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

Until the 2023/24 season, he was a permanent member of the ensemble at the Staatstheater am Gärtnerplatz in Munich, where he sang the Sprecher in Die Zauberflöte, Masetto and Leporello in Don Giovanni, Don Basilio in Il barbiere di Siviglia, Alidoro in La Cenerentola, Monterone in Rigoletto, Count von Walter in Luisa Miller and Frank in Die Fledermaus, among others.

His concert activities include national and international performances such as various lieder recitals, Beethoven's 9th Symphony in Bangkok, Lisbon and at the Grosses Festspielhaus Salzburg, the Johannes Passion by J. S. Bach and Handel's Messiah in the Vienna Konzerthaus, Mozart's Requiem in Germany, Mendelssohn's Paulus in the Golden Hall of the Vienna Musikverein and further performances in countries such as Italy, Hungary and Poland as well as two appearances at the open-air concerts "Klassik unter Sternen" and "Klassik in den Alpen" by KS Elīna Garanča in summer 2019.

In the 2024/25 season, Alexander Grassauer is "Young Talet" of the Konzerthaus Wien, where he will perform in various concert formats. He will return to the Gärtnerplatztheater in Munich as a guest to take on the role of Dulcamara in Donnizetti's Elisir d'amore, among others. At the Vienna Kammeroper, he will take part in the modern opera Der Prozess by Gottfried von Einem.

Alexander Grassauer is a laureate of several international vocal competitions. He won first prizes at the 2017 Hariclea Darclée Singing Competition in Romania, the 2017 Brahms International 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 Elīna Garanča's Future Voices initiative.