With reference to a wheel used as an instrument of torture, the phrase to break a butterfly on a wheel, and its variants, mean to use unnecessary force in destroying something fragile.

The earliest occurrence of this phrase that I have found is from An Epistle from Mr. Pope, to Dr. Arbuthnot (London: Printed by J. Wright for Lawton Gilliver, 1734), by the English poet Alexander Pope (1688-1744)—who perhaps coined to break a butterfly on a wheel:

Let Paris tremble—“What? that Thing of silk,
“Paris, that mere white Curd of Ass’s milk?
“Satire or Shame alas! can Paris feel?
“Who breaks a Butterfly upon a Wheel?”
Yet let me flap this Bug with gilded wings,
This painted Child of Dirt that stinks and stings;
Whose Buzz the Witty and the Fair annoys,
Yet Wit ne’er tastes, and Beauty ne’er enjoys,
So well-bred Spaniels civilly delight
In mumbling of the Game they dare not bite.

In A Short Introduction to English Grammar: With Critical Notes (London: Printed for A. Millar, and R. and J. Dodsley, 1763), the English clergyman and literary scholar Robert Lowth (1710-1787) wrote that Alexander Pope’s formulation ought to be corrected:

          “Who breaks a butterfly upon a wheel?” Pope.
It ought to be the wheel; used as an instrument for the particular purpose of torturing Criminals: as Shakespear ¹;
          “Let them pull all about mine ears; present me
           Death on the wheel, or at wild horses heels.” ²

¹ Shakespear is one of the spellings of the Swan of Avon’s surname that have existed in the course of time.
² This is a quotation from The Tragedy of Coriolanus, by the English playwright and poet William Shakespeare (1564-1616).

In The Works of Alexander Pope Esq. Volume IV. Containing his Satires, etc. (London: Printed for A. Millar, J. and R. Tonson, C. Bathurst, H. Woodfall, R. Baldwin, W. Johnston, B. Law, T. Longman, T. Caslon, Johnson and Davenport, and M. Richardson, 1766), the English clergyman, author and literary critic William Warburton (1698-1799) drew an interesting parallel between two passages from Alexander Pope’s works:
– ““Who breaks a Butterfly upon a Wheel?” / Yet let me flap this Bug with gilded wings, / This painted Child of Dirt that stinks and stings” from An Epistle from Mr. Pope, to Dr. Arbuthnot;
– “Ye tinsel Insects! whom a Court maintains, / That counts your Beauties only by your Stains, / Spin all your Cobwebs” from One Thousand Seven Hundred and Thirty Eight. Dialogue II. (Dublin: printed by R. Reilly. For G. Risk, G. Ewing, W. Smith, and G. Faulkner, 1738):

These (it has been objected) are Insects not of Nature’s creating, but the Poet’s, and therefore such compound images are to be condemned. One would think, by this, that mixed qualities troubled the sense, as much as mixed metaphors do the style. But whoever thinks so, is mistaken. The fault of mixed metaphors is, that they call the imagination from image to image, when it is the writer’s purpose to fix it upon one. On the contrary, mixed qualities do their office rightly, and inform the understanding of what the Author would insinuate, that the moral insect is a more worthless creature than the physical, as he collects together, in one individual, divers bad or trifling qualities, which Nature had dispersed in many. And when, in fact, we see them so collected; as venom, sophistry, and insidiousness, in a Court-Butterfly, the giving it the bite of the bug, and the web of the spider, makes it a monster indeed, but not of the Poet’s creating, but only of his naming.

These are, in chronological order, the other earliest occurrences of the phrase to break a butterfly on a wheel, and variants, that I have found:

1-: From the concluding lines of the Preface to Thomas and Sally: Or, The Sailor’s Return. A Musical Entertainment. As it is performed at the Theatre Royal in Covent-Garden (London: Printed for G. Kearsly and J. Coote, 1761), by the Irish playwright Isaac Bickerstaffe (1733-1808?):

To conclude. The author thinks there is no doubt, on account of the music, which is admirable; and the performance, which will be excellent; but this little piece must come off well upon the stage; but after having been acquitted there, he foresees, some busy people will be for bringing it before the judges in the court of criticism. Now he applies himself to the said judges, requiring them to consider all such proceedings as arbitrary, at least, if not unprecedented: He desires, that they will suffer the insignificancy of this piece, to screen it from their cognizance; and that they will not attempt to break a butterfly upon a wheel.

Note: The phrase is to break a butterfly on the wheel in the Preface to Thomas and Sally: Or, The Sailor’s Return, as published at Belfast in 1767 by James Magee.

2-: From The Beauties of all the Magazines selected (London, England) of June 1764:

From the St. James’s Magazine.
To the Author of a literate, alliterative Bard.

Tho’ satire runs a muck about the town,
Cuffs strong mens [sic] ears, and knocks poor weak ones down;
Rolls them, in sport, or malice, in the dirt,
Spoiling their cloaths, it seldom does them hurt:
Nay e’en the mighty Juvenal of the age,
Hath shewn some marks of pity in his rage,
But thou, inhuman butcher as thou art,
Play’st not the ruffian’s but the hangman’s part.
A true high-dutch jack-ketch, expertly bred
To cut men up, alive; and spit them, dead.
What had the harmless hapless L——e done?
Where is the crime of pedantry and pun,
That thou shouldst thus, with more than savage fury,
Condemn the culprit without judge or jury;
Then hang him up, as ’twere in mere terrorem,
With all his virtues strung like crimes before him,
In th’ iron chains of damn’d alliteration,
A living laughing-stock for all the nation?
Was it for thee, (who hast so long giv’n o’er
The play of rhime to tend the sage’s lore)
Howe’er provok’d, to dip thy sober pen
In the foul ink of squabbling wits again?
Was it worth while to make a glow-worm feel,
Or break a butterfly upon a wheel?
No, let the harmless insects sport or shine,
Long as their day is fair or evening fine;
Full moon, their summer past, their feeble ray
Will cease to blaze, their flutt’ring wings to play:
Let then the poor ephem’rons have their flight,
They only live, alas! from morn to night:
And, tho’ they buz, while hov’ring on the wing,
They’re merely drones, that neither work nor sting.
Wave but a fly-flap, and you lay them low,
Ending their puny beings at a blow.
Charles Churchill’s ³ muse, should e’er he so incline,
Could damn ten thousand of them in one line.

³ Charles Churchill (1732-1764) was an English poet and satirist.

3-: From the review of The Life of Cardinal Reginald Pole, written originally in Italian, by Lodovico Beccatelli, Archbishop of Ragusa; and now first translated into English. With Notes Critical and Historical. To which is added, an Appendix, setting forth the Plagiarisms, false Translations, and false Grammar in Thomas Phillips’s History of the Life of Reginald Pole. By the Reverend Benjamin Pye (London: Printed and sold by C. Bathurst, 1766)—review published in The Critical Review: Or, Annals of Literature (London, England) of April 1766:

If Dr. Pye has examined the compositions of Beccatelli and Phillips with the accuracy he has discovered in this performance, merely to prove that Pole was both a weak and a wicked man, we think his labour has been misapplied. The history of his negociations abroad prove him to be the first, and his administration in England convinces us he was the latter, so that our ingenious translator, editor, and annotator, has, in fact, done no more than “broken a butterfly upon a wheel.”

4-: From Letter X, in Je ne sçai quoi: Or, A collection of letters, odes, &c. Never before published. By a Lady (London: 1769), by Anne B. Poyntz:

Thus have I endeavoured, though faintly indeed, to picturize a man (if he may merit such a name), and in such indelible colours too, that he may never impose on you, as he has done so fatally on many; and hope, as you know the wretch, by sight at least, that you will say I have painted him in his own proper colours—and would to Heaven I could immortalize him in verse, as Pope does, when he says,
           Whoe’er offends, at some unlucky time,
           Slides into verse, and hitches in a rhime. ⁴
Yes, he should hitch so as never to extricate his dear self; and, though a woman, would I contradict this great writer, and, for once, would break a butterfly upon a wheel.

⁴ This is a quotation from the Imitations of Horace (1733-38), by Alexander Pope.