What's ironic about Proctor's "black mischief" comment and Cheever arresting Elizabeth in The Crucible?

The irony behind Proctor's condescending label of 'black mischief' with regard to the trials was to suggest that they were not fair trials, but a mockery of a trial. These 'trials' had nothing to do with 'the truth', instead they were orchestrated to promote hysteria within the community by suggesting certain people in the community were acting upon satan's instruction, and as such had to be exposed and punished because their actions or beliefs differed from that of the status-quo. The idea of promoting an unfounded fear within a society in order to side-track them from the reality of their true circumstances can work well if delievered in what looks like a just and noble cause. Remember, Arthur Miller wrote this novel in order to highlight the actions of what Senator Joseph McCarthy and his Committee of Un-American activities was doing in 1957. His novel was set in the past, however his intent was clearly meant as a wake-up call for the 1950's American society. Miller uses Cheever to epitomize hypocrisy, however worse than that in the 1950's Miller suggests people might not be everything they seem...

Ironic typically means that something occurs that is the opposite of what you might have expected.  So, witchcraft itself is usually referred to as a black art; in fact, Danforth even asks Proctor if he keeps his "black allegiance" to the devil.  So the fact that John calls the trials a black mischief is taking the descriptors that are usually reserved for witches, and placing it on the people that are condemning others for witchcraft.  You would expect that the trials would be a beacon of truth and sanity; ironically and unfortunately, they aren't in this historic situation.

As for Cheever arresting Elizabeth, that is ironic because it is hinted that Cheever is good friends with the Proctors.  In fact, Elizabeth herself tells John, "Let you go to Ezekiel Cheever-he knows you well", wanting John to tell him what Abby said.  Elizabeth feels that Cheever will be able to help John to vindicate the honor of those women accused.  Ironically, it is Cheever himself that comes, not to help, but to arrest Elizabeth.  This must have been a hard blow for the Proctors, to see a friend so taken by the courts.

Is it ironic that Ezekiel Cheever arrests Elizabeth Proctor in The Crucible?

Early in act 2, Elizabeth Proctor urges her husband to approach the Salem court to tell the officials that Abigail Williams has told him that what the girls were doing in the woods had nothing to do with witchcraft. John Proctor is reluctant to tell the court that the girls' accusations are fraudulent because he has no proof. He and Abigail were alone when she told him.

Elizabeth presses him, saying, "Let you go to Ezekiel Cheever—he knows you well." It is ironic that it is Ezekiel Cheever who comes with the warrant to arrest Elizabeth Proctor at the end of act 2 because Abigail Williams has accused Elizabeth. Prior to her arrest, Elizabeth Proctor had believed that Cheever would have taken the word of John Proctor against the girls. The man whom she thought might be their ally is instead the one who comes with a warrant for her arrest and discovers the "evidence" of the poppet.

Irony exists when there is some discrepancy between expectation and reality.  In Act Two, when Cheever arrives at the Proctors' home to arrest Elizabeth, Giles Corey says, "It's a pity, Ezekiel, that an honest tailor might have gone to Heaven must burn in Hell.  You'll burn for this, do you know it?"  It does defy expectation, somewhat, to have a tailor making arrests on behalf of the court, but it definitely defies expectation to have an honest man working for a corrupt court.  Further, there is a great deal of irony in the fact that the court accepts the (untrue) words of the girls as fact, and then a very honest woman -- Elizabeth -- is accused and not believed.  Corey's comment shows that one would have expected Cheever to go to Heaven before, but, now, because of this new work that he does, he will instead go to Hell.  Therefore, there is some irony in his new position as well as in her arrest, but not necessarily because of the fact that it is he who arrives to arrest Elizabeth.