This is a great question! We need to remember the point of view adopted in this great story. Poe writes using first person perspective, and in addition, if you are a shrewd reader, you will notice that he assumes the voice of an unreliable narrator - a narrator whose trustworthiness and reliability we come to doubt through what he says and his account of the story. Centrally, it becomes increasingly clear that we are presented with a narrator who is insane, and this insanity is presented partly through the use of punctuation in his account, especially focussed on the use of the dash to indicate his frenzied emotions. Consider this excerpt from the last paragraph of the story:
Oh God! what could I do? I foamed - I raved - I swore! I swung the chair upon which I had been sitting, and grated it upon the boards, but the noise arose over all and continually increased. It grew louder - louder - louder! And still the men chatted pleasantly, and smiled. Was it possible they heard not? Almighty God! - no, no! They heard! - they suspected! - they knew! - they were making a mockery of my horror! - this I thought, and this I think.
You would do well to ask yourself what is the effect of all of these hyphens in this block of text. They seem to emphasize the heightened emotions of the narrator, especially his intense agitation, his dislocated thoughts and the way that the sound of the heartbeat is impacting him. Clearly, then, the use of punctuation could be said to highlight the insanity of the narrator, underlining his unreliability.