Babayan was born on 5 March 1965 in Stepanakert, Nagorno-Karabakh. In 1982, he finished Armenian secondary school # 7 named after Eghishe Charents in Stepanakert. From 1983 to 1985, he served in the Soviet military contingent in Eastern Germany .
In 1988, Samvel Babayan enlisted in a paramilitary unit and rose to command his own unit and leading it professionally. From 1989 to 1991 he was the commander of the Stepanakert second Volunteers Company and a member of the Stepanakert underground central headquarters. Lieutenant General Samvel Babayan rose to prominence during the military phase of the Nagorno-Karabakh conflict, in 1991-1994. Babayan carried out coordination of Armenian operations in Karabakh, participated in the development of the plan to capture Shusha and was the commander of the front of Lachin. As unified military command began to be established in Nagorno Karabakh in 1992-1993, Babayan became the Commander of the Nagorno-Karabakh Defense Army in 1993, after his predecessor Serzh Sargsyan left to become Armenia's Defense Minister. Under his command, the Karabakhi military succeeded in winning a number of strategic battles against the Azerbaijani military and regained control over most of Nagorno-Karabakh as well as partially controlling 7 districts of Azerbaijan.
By December 1999, Babayan was forced to relinquish his position as the Self-Defense Forces Commander. Armenian president Robert Kocharyan's precarious position in post-27 October political environment did not allow him to tackle the Babayan issue directly, leaving it to the unrecognized government of Nagorno-Karabakh under president Arkadi Ghukasyan and the new Karabakh Army leadership. On 22 March 2000, Babayan allegedly launched an assassination attempt on Arkadi Ghukasyan, leaving the president seriously wounded but alive.
At the 26 February session on the case of the 22 March 2000 assassination attempt against Arkadi Ghukasyan in Stepanakert, the sentences for the 16 defendants were read out loud. Babayan was sentenced to 14 years in prison.
During the investigation and in jail, Babayan's health greatly deteriorated. He was said to suffer from hepatitis and other ailments which could not be treated in prison. On 18 September 2004, Samvel Babayan was released from maximum-security prison in Shusha due to health concerns, with the terms of release including a probationary period and continued disenfranchisement.
In November 2005, Samvel Babayan founded the Dashink political party with his supporters. The party did not achieve any major success.
Babayan returned to Armenia in May 2016 after a de facto exile in Moscow, shortly after major clashes in Nagorno-Karabakh line of contact. He stated, "Whether I was in Karabakh, Armenia or abroad, the security concerns of my country, my people have always been on my mind. I have the full grasp of the military situation, the problems at the frontlines and possess all necessary information."
Samvel Babayan has been the holder of such titles as Commander of Self-Defense Forces of Nagorno-Karabakh and Minister of Defense. Babayan has been awarded with the army ranks of lieutenant colonel (1992), colonel (1993), major general (1994) and lieutenant general (1996). He has been awarded with the Golden Eagle medal of the Nagorno-Karabakh Republic (1997) and has been declared a Hero of Artsakh. He is married and has three children. His brother Karen is the former Mayor of Stepanakert and Minister of Internal Affairs of the Nagorno-Karabakh Republic.