Hamlet impulsively stabs Polonius, who is hiding behind an arras in Gertrude's room, because he believes that Polonius is Claudius. Hamlet unintentionally kills Polonius, and the accident is nothing short of mistaken identity.
Hamlet has recently witnessed his uncle react to the Mousetrap scene, which confirms the ghost's message that Claudius assassinated his father. Hamlet is bent on revenge but continually hesitates to act. Hamlet hesitates to act because he has moral reservations, fears that he will doom his soul, and understands the consequences attached to killing a king.
Before accidentally killing Polonius, Hamlet passes a perfect opportunity to murder his uncle while he is praying, because he does not want Claudius's soul to go to heaven. Once Hamlet enters Gertrude's chamber, he accosts his mother for marrying his uncle. Gertrude is particularly disturbed by Hamlet's aggressive demeanor and fears for her life. It is important to note that Gertrude believes that Hamlet is insane and capable of anything.
Hamlet suddenly shoves his mother, who screams for help, and Polonius gives his position away by calling from behind the arras. Hamlet reacts rashly by stabbing at the arras and killing Polonius. Hamlet was under the impression that Claudius was behind the arras. Upon murdering Polonius, Hamlet hides his body and offends Laertes by refusing to allow his father a proper burial. Claudius takes advantage of Hamlet's mistake by persuading Laertes to avenge his father's death.
Further Reading
Hamlet kills Polonius because he thinks that Polonius is the king, Hamlet’s Uncle Claudius, who has recently revealed through his guilty behavior that he murdered Hamlet’s father, Claudius’s own brother—confirming what the ghost of Hamlet's father said at the beginning of the play. In this scene, Hamlet’s mother, Gertrude, has summoned Hamlet to her room to have a conversation about his behavior, which displeases her. On his way to her room, Hamlet sees his uncle in a vulnerable position (praying) but decides not to kill him just then because he does not want to send his uncle straight to heaven. He believes this his uncle may be confessing his sins and asking God’s forgiveness, so Hamlet plans to wait until he can catch his uncle when he is “full of bread” (sins), as Hamlet's own father was when he was murdered (3.3.85). (This resulted in his father being sent to Purgatory, it seems, until his sins are burned away and his soul is prepared to enter heaven.)
When Hamlet and Gertrude begin to talk, Hamlet scares her and she cries out; this results in Polonius, who is hiding behind an arras (tapestry) in the queen’s chamber, to cry out as well. Hamlet, believing that it is the king in hiding, stabs Polonius through the tapestry and kills him. He’d hoped to kill the king while he was in the middle of committing some sin, so he didn’t wait to investigate before acting.
In act three, scene two, Hamlet has the perfect opportunity to kill Claudius but refrains...
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from taking action because Claudius is in the middle of praying. Hamlet justifies his lack of action by commenting that he does not want Claudius's soul to go to heaven.
In the next scene, Polonius hides behind a tapestry in Gertrude's chamber while she has a private conversation with her son. At the beginning of their conversation, Hamlet severely chastises Gertrude and forcefully tells her that she cannot leave until he holds a mirror to her soul, which influences Gertrude to cry out for help. Upon hearing Gertrude's cries, Polonius yells from behind the tapestry, and Hamlet instinctively thrusts his sword through the tapestry, killing Polonius. Hamlet believed that Claudius was spying on him from behind the tapestry and hoped to kill his unscrupulous uncle. However, Hamlet accidentally kills Polonius and proceeds to carry on his conversation with Gertrude before hiding the counselor's body.
Overall, Hamlet accidentally kills Polonius after mistaking him for King Claudius, who he believes is spying on him from behind the tapestry in Gertrude's chamber.
Hamlet kills Polonius in act 3, scene 4 of William Shakespeare's Hamlet because he believes him to be King Claudius, the man who killed Hamlet's father and against whom Hamlet spends the entire play seeking revenge.
The scene is set within Queen Gertrude's closet, and Polonius is there eavesdropping on the conversation because he, like many others in the castle, believes Prince Hamlet to be descending into madness. Polonius hides behind a curtain so as not to be seen. Hamlet, for his part, believes he and his mother are alone and takes the opportunity to confront her about the death of his father and her subsequent marriage to his uncle. The confrontation grows violent as Hamlet becomes more and more agitated, and Gertrude cries for help. Polonius finally makes his presence known, trying to help his queen, but before he can get out from behind the curtain, Hamlet, already enraged and believing him to be Claudius, stabs Polonius to death.
When the curtain is drawn back and Polonius's body is revealed, Hamlet regrets his rash actions:
Thou wretched, rash, intruding fool, farewell!I took thee for thy better
Throughout the first three acts, Hamlet struggles to act on the suspicion of his uncle's villainy, and then when he finally does, he acts rashly, and the wrong man pays for Claudius's crimes.
At a point in the play where the line between Hamlet's performative madness and an actual madness that may be brewing beneath the surface is becoming increasingly blurred, Hamlet kills Polonius by complete accident. While Gertrude and Hamlet are arguing heatedly, Polonius is spying from behind a tapestry. Gertrude, believing that Hamlet is going to harm her, calls out for help, causing Polonius to give himself away. Hamlet, believing that the figure behind the curtain is Claudius, stabs at it wildly. Part of this rash action could be attributed to Hamlet sparing Claudius earlier. Despite having the perfect opportunity to kill him, he did not want to go through with it while Claudius was praying. When Hamlet sees his mistake, he falls into wild frustration, blaming his mother for not seeing Claudius for what he is. The ghost enters and reprimands Hamlet, but as Gertrude cannot see the ghost, Hamlet seems to be madly talking to himself.
Hamlet actually kills Polonius by mistake. When he hears the noise and movement coming from behind the curtain, he thinks it is his uncle, the king. He has decided he wants to kill the king, as you probably know. So he thrusts his sword into the curtain, thinking he is killing his uncle, and then it turns out to be the wrong person.
Polonius was hiding there spying, so it falls onto him, really. But because of this murder, it triggers Polonius' son to come back to avenge his father's death, leading to the highly dramatic ending of the play.
So to answer your question, he does it because he thinks it's his uncle, the king, hoping to finally get revenge on his uncle for killing his father.
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