Armenian-born Pushman studied at the Constantinople Academy of Art before he left for the United States at the age of seventeen. After teaching art in Chicago he went to Paris to further his own training with the esteemed professors at the Academie Julien. He opened his own studio in 1921, and began painting what would become the focus of his career: Oriental-motif still lifes and portraits. It was the famous teacher Robert-Fleury who recognized his talent for this specialized subject matter, and Pushman turned his fascination with Asian mysticism into a successful career. He exhibited and won the silver medal at the Paris Salon in 1921. Upon his return to the States, he was met with eager audiences across the country, in Chicago, Southern California, and New York City. In New York Pushman often exhibited his works at the Grand Central Art Gallery, where at his solo show in 1932, each and every painting was sold on the opening day.
His works are housed in a great number of important collections, including those at the Metropolitan Museum, New York, NY; the Museum of Fine Arts, Houston, TX; the Museum of Fine Arts, Boston, MA; the Nelson-Atkins Museum of Art, Kansas City, MO; and the Milwaukee Art Museum, Milwaukee, WI.