Whether or not Willy fits the definition of a tragic hero is actually a much debated point. In his own article "Tragedy and the Common Man," which appeared in The New York Times in 1949, Arthur Miller certainly stated that he attempted to portray the common man as a tragic hero in Death of a Salesman. He argued that tragedy is seen when a character is willing to "lay down his life" for the sake of "his sense of personal dignity." We see Willy commit suicide by crashing his car after loosing his job in order to secure $20,000 in insurance money, thus providing for his family and giving Biff something to start his business with. His dignity was saved because even though he felt like a failure, his death was worth something.
However, other scholars would disagree with Miller's interpretation and presentation of a tragic hero. According to Aristotle, a tragic hero is a noble person, often a great political hero. Even if we agree with Miller that a tragic hero can be a common man instead of king or other high-ranking figure, the hero must still be a noble, just, and morally up-right person. Willy fails in this instance because he cheated on his wife, a huge reason for Biff's emotional and psychological struggles. Furthermore, Willy lost his life due to suicide, even making several suicide attempts before finally succeeding. Suicide is not generally accepted as a virtuous activity. While we often see tragic heroes commit suicide, such as Antigone, it is only because their lives are already threatened. In the case of Antigone, her true tragedy is that she was judged too harshly and condemned to a harsh death of starvation in a tomb. Hence, she decided to take her own life through the quicker, less painful means of hanging. Loss of job, like Willy lost his job, does not seem like a just and noble reason to commit suicide. Hence, Willy does not fit Aristotle's definition of a tragic hero because he is not noble and virtuous.
Also according to Aristotle's definition, a tragic hero's downfall stems from mistakes made through freedom of choice. Bert Cardullo of The Columbia Journal of American Studies points out that Willy does not even fit this definition because Willy felt that he had no other courses in life. He very passively accepted working himself to a state of exhaustion and choosing to kill himself (Cardullo, "Death of a Salesman and Death of a Salesman"). The character Biff, however, may dispute Cardullo's point. Biff makes it clear that he thinks his father made all the wrong decisions. He felt that his father should not have been a salesman, but would have been better off as a carpenter instead. If we are to agree with Biff, then we can argue that Willy's choices led to his tragic end, rather than agree with Cardullo who stated that Willy really had no choice.