The question asks for three examples of either sarcasm, hyperbole or understatement in "A Modest Proposal." I have chosen three examples of sarcasm. Sarcasm means saying the opposite of what you mean. A common example of sarcasm is to say "graceful" or "great job" after somebody stumbles and falls. This is sarcasm because the speaker obviously intends to communicate the opposite of the literal meaning of the words.

Swift, filled with anger over the hard heartedness of the British toward the Irish poor, has created a narrator so clueless and without a moral compass that almost every "compassionate" statement he makes is actually meant by Swift to show the cruelty of treating the Irish as no more than objects that are only useful if they turn a profit.

Three examples of sarcasm are the following: 

"Thus the Squire will learn to be a good Landlord, and grow popular among his Tenants." This statement is in praise of a landlord buying and eating the year-old children of his tenants, something that would, in reality, be considered horrible and cruel to do. 

"And besides it is not improbable that some scrupulous People might be apt to Censure such a Practice, (although indeed very unjustly) as a little bordering upon Cruelty, which, I confess, hath always been with me the strongest objection against any Project, how well soever intended."

The narrator makes the above statement about selling 12-year-olds as food for the rich. This statement also includes understatement, as it is far more than bordering upon cruelty to eat a child, but the end of it, in which the narrator says cruelty has always been his strongest objection against any project, is clearly meant by Swift to be sarcastic, for all of the narrator's projects are unspeakably cruel.

Some Persons of a desponding Spirit are in great concern about that vast Number of poor People, who are aged, diseased, or maimed, and I have been desired to imploy my thoughts what Course may be taken, to ease the Nation of so grievous an Incumbrance. But I am not in the least pain upon that matter, because it is very well known, that they are every Day dying, and rotting, by cold, and famine, and filth, and vermin, as fast as can be reasonably expected. And as to the younger Labourers they are now in almost as hopeful a Condition. They cannot get Work, and consequently pine away from want of Nourishment, to a degree, that if at any time they are accidentally hired to common Labour, they have not strength to perform it, and thus the Country and themselves are happily delivered from the Evils to come.

Swift is being sarcastic in having his narrator praise as "hopeful" the fact that the poor, old and young, are dying off in horrible conditions as quickly as possible.

The narrator of this pamphlet, having made his proposal that the poor Irish sell their one-year-old babies as a food source to the rich English, states, "I grant this food will be somewhat dear, and therefore very proper for landlords, who, as they have already devoured most of the parents, seem to have the best title to the children." The first part of this statement constitutes an understatement: he says the food (meat from the carcasses of dead babies) will be "somewhat dear," meaning it will be somewhat valuable. I would venture to say the living baby would be considered very dear to its parents. Swift suggests that the child's only value lies in its cost as a sellable commodity when, in fact, we (and Swift) can all agree, I hope, that a child's life has a great deal more value than this.

The second part of the statement, that landlords "have already devoured" the parents of the children who would be sold in such a manner, constitutes hyperbole. The narrator doesn't mean that the landlords have literally eaten up these poor Irish parents; instead, Swift uses this crafty word choice as a way to point out that this proposal is only making literal what the English have already figuratively done. They have consumed Ireland by buying up all the land and taking food from the mouths of the Irish. The Irish get thinner as the English get fatter. It's an exaggeration, to be sure, to say that the English devour the Irish, but not much of one.

Toward the end of the essay, the narrator says, "let no man talk to me of [other] expedients, 'till he hath at least some glympse of hope, that there will ever be some hearty and sincere attempt to put them into practice." This line comes after he has already listed a great number of other ways the Irish could acquire more money, the government could run more efficiently, and the English could show some mercy and compassion. His insistence that there is no hope that any of these ideas had been or would be honestly tried constitutes sarcasm on Swift's part. He is blaming the Irish, in part, for their own troubles, and he blames the English for exploiting the Irish into the grave for their own personal gain. No one escapes Swift's scorn.