This is an interesting question, if only because there is some doubt about whether a tragedy (as compared to a melodrama) is possible in our world. Miller addressed this very question in an essay, "Tragedy and the Common Man."
From one point of view, Willie lacks the nobility that is generally attributed to the "tragic hero." Tragedy is generally thought to revolve around a character who we view as our "better" (is this possible in a democracy) who, despite nobility of character, has a flaw that leads to his/her downfall: Macbeth/ambition; Othello/ jealousy; Hamlet/indecision etc.
Many people see Willie as a pathetic figure, not a tragic one. He does not have the nobility of character that would cause us to have one of the classic responses to tragedy: if that could happen to such a noble character, what could happen to me?
In his essay, Miller argues that "The quality in such plays that does shake us, however, derives from the underlying fear of being displaced, the disaster inherent in being torn away from our chosen image of what or who we are in this world. Among us today this fear is as strong, and perhaps stronger, than it ever was. In fact, it is the common man who knows this fear best." If you accept this as a definition of tragedy, Willie certainly is a tragic figure as he learns that he has "been torn away from [his] chosen image of who [he] is.
Room for a great discussion.
In a tragedy, the story details the downfall of the protagonist, known as the tragic hero. This character fails as a result of a tragic flaw in his/her personality; in other words, the character causes his/her own downfall.
Willy is plagued by an American Dream that is unrealistic and impractical. He is obsessed with glitz and glamour, wanting success through recognition. This is why he is so focused on Biff. Biff was a high school football star and seemed to have the makings of an all-American hero. Willy, who had yet to fill out that particular role, put all his hopes into his son. As Willy gets older, he sees his life dwindling away but his dream no closer. But instead of accepting and creating a new dream, Willy clings tightly to the hopes he once had. This causes his despair, which leads to his suicide. He is a tragic hero.
How does Death of a Salesman subvert in conventions of a tragedy?