To answer the question effectively, one first needs to define tragedy in the context of literature. In this regard then, tragedy is defined as drama which depicts human suffering and as such, leads to a catharsis within the audience. This means that by watching the play, the audience would experience either intellectual enlightenment or the purification and purgation of emotions. This suggests that we, the audience, would be able to either be awakened intellectually to a new perspective or that we will, through identification with or empathy for the characters in the play, find a release for our own feelings.
The play The Crucible more than adequately subscribes to this definition. There are a number of examples of human suffering depicted in the play. When the accusations start and people are arrested, we are exposed to their suffering. What gives greater depth to the pain experienced by the characters is the fact that they are all innocent. Their attempts to proclaim their innocence are dismissed. There is no concrete evidence to prove their guilt. Furthermore, their only hope is to confess to something they did not do, ensuring spiritual, but not physical, redemption - many were incarcerated after their confessions. Such was the tragedy of John Proctor, for even after having publicly "confessed," he was still hanged only because he refused to sign the confession.
The tragic death of Rebecca Nurse is another example. She had a good name in the town and was much admired and respected, so much so that most of the townsfolk went to her for advice and consultation. People respected her integrity and deemed her kind and generous. Her death is therefore one of the most tragic. She died because of the Putnam's jealousy and their greed for property. Their accusations were believed and they went as far as using their daughter to lie to the court.
The executions of Martha and Giles Corey add to the tragedy. What makes Martha's death more poignant is that her husband inadvertently implicated her by referring to her interest in books and that he would, at times, be unable to speak in her presence. Little did he know that his attempts at trying to gain clarity about these incidents would eventually result in his wife's and his own deaths. One can only be shocked at the utter brutality of Giles' execution; he was pressed to death. He refused to confess and died an innocent man. He also was a victim of the Putnams' greed. The Putnams' used the witch trials to gain an advantage and their plotting and scheming were a tragic success.
There are many other examples of tragedy in the play: Tituba, Sarah Good, Mr. Jacobs and others. The greatest tragedy, however, is encompassed in John Proctor's chilling cry:
"I’ll tell you what’s walking Salem - vengeance is walking Salem. We are what we always were in Salem, but now the little crazy children are jangling the keys of the kingdom, and common vengeance writes the law!"
It isn't even that Proctor dies, but it is the reason he dies. One of Proctor's tragic flaws is an inability to rationalize the world around him. He was unable to rationalize his feelings about Parris with his need to be a part of the community. He was unable to rationalize Elizabeth's distance from him, and turned impetuously to Abigail. And in the end, he is unable to rationalize the signing of the paper. It is a moment of strength for him, but it is also a flaw which brings about his death.
In addition to Proctor's hanging, you have the tragedies that befall his wife Elizabeth. In spite of being a good moral woman who would protect her husband even if the cost is her own life, she is still falsely accused of witchcraft and imprisoned. At the end of the play, she is left without her loving husband who was everything to her. Of course, you have the larger, surrounding tragedy, which is all the innocent people who were accused of witchcraft during that time and imprisoned or killed, solely based on a hysteria started by bored teenage girls.