Harutyunyan's Armenian Lullabies was recognized by the New York Times as an outstanding world music CD in 2004.

[2] Before performing with the Shoghaken Ensemble, Harutyunyan performed as a soloist with the Agunk Ensemble (founded by Hayrik Mouradian) of Armenian National Radio in Armenia, Europe, and the Soviet Union.

With Shoghaken, she has performed in Armenia, France (including a 2006 performance at the Théâtre de la Ville in Paris), Germany, Estonia, Russia, the United Arab Emirates, and the U.S. (including an eighteen-concert 2004 tour and an appearance at the 2002 Folklife Festival as part of the Silk Road project organized by Yo Yo Ma).

In autumn 2009, Hasmik performed in concerts in the USA with the Kitka Women's Vocal Ensemble, presenting the music of Komitas, Hayrik Mouradian, and Armenian lullabies, as well as participating in the San Francisco World Music Festival.

In 2010, she performed with Shoghaken and gave a workshop on Armenian folk song and dance in Ljubljana, Slovenia.