In his satiric poem "Epistle to Dr. Arbuthnot," the speaker, likely Pope himself, addresses a friend and does plenty of complaining about how he is continually annoyed by beginning poets who are always coming to him for advice. He does not have a moment's peace.
Pope begins by telling his friend to shut the door. He is exhausted. He continues with the order "Tie up the knocker." His friend should say that he is sick or even dead, for he feels like the insane asylum has let out all its inmates and they are all showing up at his door with "fire in each eye, and papers in each hand," longing for his guidance and critiques. "They rave, recite, and madden round the land," he remarks.
What's more, Pope feels like he has nowhere to hide. These budding poets are on the attack, and he cannot escape. They charge at him from all directions. He can't even escape them by going to church. Not even the Sabbath day is free of bothersome verse-makers. In fact, right in the middle of Pope's dinner, one of these poets shows up.
This "man of rhyme" is "from the Mint." He is a poet—or at least he thinks he is—but one who is focused primarily on making money by his writings. This is why Pope says he is "from the Mint." A mint is a place where money is printed and coins are produced. This fellow, like all the rest, is seeking Pope's advice and help with his poetry. He doesn't seem to care at all that Pope is trying to relax and eat his dinner.
Pope goes on to complain that none of these people are really poets. They merely scrawl along on their papers and then run to him "to keep them mad or vain." They want his approval and his guidance. Then when they don't hear what they want to hear, they turn against Pope and criticize his works and curse him. No wonder he is fed up!