It depends how you define tragedy.
According to Aristotle's famous definition of tragedy, no. Miller's play does not depict the fall of a "great man" in the traditional sense (Willy Loman is neither king nor nobleman, nor has he really achieved anything) nor does the action take place within classical unities (that is, the action jumps forward in time, and place). Don't be drawn into "tragic flaws" - they are a misreading of Aristotle's text.
Miller himself, on the other hand, in his essays on "Modern Tragedy" and "Tragedy and the Common Man" argues that tragedy *can* and *should* deal with the plight of working class, ordinary characters like Loman as tragic protagonists - and that their suffering is as profound as that of a king. Miller's arguments for a democratising of tragedy were echoed in Raymond Williams' book "Modern Tragedy". Williams' arguments would classify "Death of a Salesman" as a tragedy.
So the answer to your question is that it depends who you believe. Definitions of tragedy are notoriously complex - so much so that at the University of Cambridge, every English Lit. student has to sit an exam just on "Tragedy" and its definition!
A tragedy is usually defined as a piece of literature which contains somber theme, typically that of a great person destined through a flaw of character or conflict with some overpowering force, as fate or society, to downfall or destruction. Although Willy Loman is not a "great person" in the usual sense, he is certainly representative of many others who tried to reach the American Dream but simply could not achieve it. His dreams, like many others, have a tremendous impact on his family. However, another clue to the play's classification is the author's intent. The playwright, Arthur Miller, subtitled the play "Certain Private Conversations in Two Acts and a Requiem". A requiem is a ceremony created for someone who has died. Usually that person is a famous or important figure. That would certainly indicate that Miller meant for the play to be a tragic commentary the effect of the American dream of success has on American society. Consequently,since Willy is representative of many people like him and their collective dreams greatly influence American society then "Death of a Salesman" is truly a tragedy.
So much of this question depends on your working definition of tragedy. Miller intends the play to be tragedy for our age. I would suggest that you consult Miller's essay "Tragedy and the Common Man" to make your own decision. The link is attached below.
Death of a Salesman is a classic American tragedy in every respect. Though the definition from Aristotle is a little antiquated, his tragic death had profound effects on the emotional feelings of everyone that watched the drama or reads it today.
Miller was a unique dramatist, who transformed the modus operandi of tragedy with his artistic genius and realistic vision. He is the true representative of modern tragedy, where tradedy does not orginate from your status or achievements, but the way you counter the uncertainity and chaos in a harsh competative world.
He is a modern Shakespeare, whose concepts are universal and applicable. The protagonist Willy Loman is searching for an economic harbour despite being a dreamer. Loman presents the terrible plight of ordinary people in these tragic words, " A MAN IS NOT A PIECE OF FRUIT. YOU EAT THE ORANGE AND THROW AWAY THE PEEL." In fact Miller presents the story of everyman in a hostile industrial set up, where there is no place for sympathy and love for the weak and the depressed classes. Hail ARTHUR for your great tagic vision. May your soul rest in peace.
like ibsen, miller often explores the origin and consequences of shameful actions