Born in Beirut, Lebanon to Armenian parents, Basmajian emigrated to Canada when he was seven years old. He was a founder of the Canadian Poetry Association, co-founder of Old Nun Publications (with Ted Plantos), and was a member of the Parliament Street Library poetry group. The Shaunt Basmajian Chapbook Award, given annually to a Canadian poet, was established in his memory. The contest ran from 1996-2008.
In 1986, he was attacked with a knife and robbed while he was driving a taxi. His right lung was punctured when a robber stabbed him.