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The phrase to cut a long story short (also, and originally, to make a long story short) means: to be brief or concise. This phrase is typically used as a sentence adverbial, with the sense: in short, in summary, briefly.

This phrase is sometimes used elliptically as long story short—for example in the following from a review of the 2009 U.S. animated film Alvin and the Chipmunks: The Squeakquel—review by Chris Wasser, published in the Evening Herald (Dublin, County Dublin, Ireland) of Thursday 17^th December 2009 [HQ Section, page 19, column 3]:

The team behind this cartoon-turned-movie franchise seem to think that they can get away with the same trick twice. That is, that it doesn’t matter how unfunny their hairy little protagonists are; they’ve got squeaky voices—sure aren’t we bound to love them? Truth be told, it’s difficult to imagine even young kids taking to this one.
Long story short, rock stars The Chipmunks enrol in your typical American high school only for a whole heap of cliché-riddled trouble to ensue.

These are, in chronological order, the earliest occurrences of the phrase to make a long story short that I have found:

1-: From The Intelligencer (Printed at Dublin. London: Reprinted, and sold, by A. Moor, 1729), by the Irish authors Jonathan Swift (1667-1745) and Thomas Sheridan (1687-1738) [No. 13: The Art of Story-Telling, page 141]:

The insipid, who may not unfitly be called Soporifick, is one who goes plodding on in a heavy dull Relation of unimportant Facts: You shall have an Account from such a Person of every minute Circumstance, which happened in the Company where he has been, what he did, and what they did, what they said, and what he said, with a Million of trite Phrases, with an and so beginning every Sentence; and to make a long Story short; and, as I was saying, with many more Expletives of equal Signification.

2-: From A Specimen of Thought upon the Gloomy Region: Or, Polyphemus Evaporated: Or, a Satiri-Tragi-Comi-Poetick Hodge-Podge and miscellaneous Poem, upon the Wooden-Man in Essex-Street (Dublin: Printed for the Author, 1732), by John Thomson [page 24]:
—Note: The Oxford English Dictionary (current online edition) erroneously attributes this text to the Scottish author James Thomson (1700-1748):

To make a long Story short, the Pope, and Pretender, and his Adherents, the French, and Spaniards, and all their united Armament at Sea and Land, are dismissed with Costs, as the Law says.

3-: From The Finesse of Rantum Scantum, a New Diverting Dialogue betwixt Tom and Harry, Fratres Fraterrimi (London: Printed for A. Hill, 1748) [page 18]—the noun juncto is a variant of junto, and the noun monasyllable is a variant of monosyllable:

Public Spirit, Fidelity, public Good, and Conscience, or Trust, &c. these are Words for the Parsons to declaim from, and enforce, in order to be well paid: But Stewards of a Club have nothing to do with such Terms nor Ideas; they are to be chiefly concern’d about fingering and keeping the Coal; and the more they save and hoard, the better Steward: They, by this, shew and make appear, they know, and love Self, and Self is nearest and dearest to us; so we must, together with our Juncto, take good Care, and be on our Guard, to preserve him, (i.e. Self) and to maintain our Power, prevent or stifle Enquiries, making a long Story short, will do it all at once; and this I will execute by turning it all upon the Hinge of Yes and No, two very important Monasyllables, at the full meeting of the Club.

4-: From The Entertaining Travels and Surprizing Adventures of Mademoiselle de Leiurich. Who travelled over Europe, dressed in Man’s Apparel, attend [sic] by her Maid-Servant as her Valet de Chambre. Now done into English from the Lady’s own Manuscript. By a Masterly Hand (London: Printed for T. Thompson, [1748]) [volume 1, page 136]:

As nothing pleases a woman’s vanity more than that her conquests should make a noise, Eliza resolved that hers should remain no longer a secret, and therefore went to visit miss Teresa a neighbour and friend, and told her all that had happened, begging she would come and see what a glorious lover she had got; miss Teresa, as she is, without dispute, one of the prettiest girls in Paris, thought it an affront to her beauty that a fine gentleman should fall in love with any but herself, and therefore resolved to try the power of her charms upon our colonel, who was so struck at her first appearance, that, notwithstanding his natural assurance which is what he excells [sic] in, he could get no farther than my god! what’s this! however, that he might give no umbrage to Eliza, he whispered in her ear, how mal à propos this girl comes to interrupt my happiness.
He then got his tongue a little untied, and said all the fine things that he had either read or could think of, and before he left the house got permission to pay his respects to Teresa at an aunt’s house with whom she lived, having neither father nor mother; but to make a long story short, (for I fear you are already tired with my colonel’s amours) I shall only tell you that poor Eliza was abandoned by this roving warior [sic], I mean he loved her no longer tho’ he continued his visits, and protested as much as ever, but Teresa was the idol of his heart.

5-: From Tristram Shandy’s Bon Mots, Repartees, odd Adventures, and Humorous Stories (London: Printed for E. Cabe, 1760) [page 44]:

When Tristram Shandy, madam, received the above invitation; which, as I said before, was written upon a card—I don’t know whether I told you it was written with the A-ch B——ps [sic] own hand or not—but, if I did tell you so, I told you a lie—for it was not written by the A-ch B——p, but by one of his grooms of the chamber—I say, madam, when Mr. Tristram Shandy received the above invitation, his heart danced hey go mad; he did nothing for two days (which shews, by the way, that there was two days between his receiving the card, and his dining with the A-ch B——p) but practice behaviour to himself—he treasured up a thousand witty sayings—and studied as hard as if he had been reading for a professorship—to make a long story short—in one word, madam, the day at last came (observe, I am not positive whether it was a sunday [sic] or not) in which he was to dine at Lambeth—and after the clock struck two, the devil could not hold him, but off he went—and, if you think proper, we will now suppose him safely lodged in the A-ch B——p’s dining room.