Groissböck was born in Waidhofen an der Ybbs in Lower Austria[4] to a doctor (father) and a teacher (mother) and was self-motivated to play piano by the age of eight.
[5] He received vocal training at the University of Music and Performing Arts Vienna where he was under guidance from Robert Holl and José van Dam.
[6] From 2002 to 2003, Groissböck was a scholar at the Eliette and Herbert von Karajan Institute and then became bass singer at the Zürich Opera House.
[11] In 2015, Groissböck sang the role of Baron Ochs at the Salzburg Festival in Der Rosenkavalier[4] after his appearance five years ago in Rusalka which at that time was directed by former Vienna State Opera director Ioan Holender.
In 2018 he gave a recital at the Frankfurt Opera, accompanied by Malcolm Martineau, which included Brahms' Vier ernste Gesänge, Robert Schumann's Liederkreis, Op.
[6] Groissböck appeared in several productions filmed at the Zürich Opera House: Don Fernando in Fidelio under the baton of Nikolaus Harnoncourt (Arthaus Musik 2004); Police Inspector in Der Rosenkavalier under Franz Welser-Möst (EMI Classics 2004); Nightwatchman in Die Meistersinger under Welser-Möst (EMI Classics 2005); the King in Aida under Ádám Fischer (ARTE France 2006); Titurel on Bernard Haitink's recording of Parsifal (Deutsche Grammophon 2007);[21] Boland in Fierrabras under Welser-Möst (EMI Classics 2007).
He sang Sarastro in Mozart's Die Zauberflöte, conducted by Roland Böer and filmed in 2011 at La Scala (Opus Arte).