Grigorian made her operatic debut in Christiansand (Norway) in 2004 as Donna Anna directed by Jonathan Miller, in 2005 she made her Lithuanian debut as Violetta also directed by Jonathan Miller, and in 2006 she became one of the founding members of Vilnius City Opera, singing in Puccini's La bohème (Mimi and Musetta), Leoncavallo's Pagliacci (Nedda), Verdi's Il trovatore, Puccini's Manon Lescaut, Tchaikovsky's Pique Dame and Eugene Onegin, Sweeney Todd, and Massenet's Werther.

She was noted in operas such as Tchaikovsky's Nastasya in The Enchantress at the Theater an der Wien in September 2014 and as Tatiana in Eugene Onegin at the Komische Oper Berlin in 2016.

[7][8] In her debut at the Salzburg Festival in August 2017, she sang the role of Marie in Alban Berg's Wozzeck to critical acclaim.

[9][10] Rupert Christiansen of The Telegraph praised Grigorian as a "superb musician, with deep understanding of Bergian vocal style".

In concert, she performed as part of the Deutsche AIDS-Stiftung [de] Gala at the Berlin State Opera, and as Marie in Drei Bruchstücke aus Wozzeck at the Teatro del Maggio and the Elbphilharmonie.

Asmik returned to the Salzburg Festival to perform the three leading roles in a new production of Puccini's Il Trittico, directed by Christof Loy.

[14][15] She returned to two of her signature title-roles this season, firstly, in Rusalka at the Dvořák Prague festival[16] and then at the Royal Opera House and secondly, in Jenůfa at the Wiener Staatsoper.