This is the definition of the American-English phrase you’ve shot, or you shot, your granny in Dictionary of Americanisms. A glossary of words and phrases, usually regarded as peculiar to the United States (New York: Bartlett and Welford, 1848), by the U.S. historian and linguist John Russell Bartlett (1805-1886):

TO SHOOT ONE’S GRANDMOTHER, is a common though vulgar phrase in New England ¹, and means to be mistaken, or to be disappointed; to imagine oneself the discoverer of something in which he is deceived. The common phrase is, ‘You’ve shot your granny.’ It is, in fact, synonymous with ‘You’ve found a mare’s nest.’ ²

¹ New England is the name of an area on the north-eastern coast of the USA, comprising the states of Maine, New Hampshire, Vermont, Massachusetts, Rhode Island and Connecticut.
² The phrase to have found a mare’s nest means to imagine that one has discovered something wonderful, which in fact does not exist; it is first recorded in the late 16^th century as to have spied a mare’s nest.

The earliest occurrence of you’ve shot, or you shot, your granny that I have found is—in an extended form—from the Wisconsin Enquirer (Madison, Wisconsin) of Wednesday 18^th March 1840:

Extract of a Letter to the Editor of the Enquirer, dated
Washington, February 24, 1840.
The House, on Monday, listened to the butt-end of jolly Tom Corwin’s ³ speech. He done a mighty big business for General Harrison ⁴; and had he not have slurred the old gentleman with his usual sarcastic tongue in the end, Gen. H. would have considered himself as a very well used man; but as it was—“Thomas Corwin, you shot your granny in the eye with a baked apple.”

³ A prominent political leader in the years before the American Civil War, Thomas Corwin (1794-1865) was at that time a Member of the U.S. House of Representatives.
⁴ A military officer, William Henry Harrison (1773-1841) became the 9^th President of the United States in 1841, but died of pneumonia a month after his inauguration.

The second-earliest occurrence of the phrase that I have found is from The Telegraph (Gloucester, Massachusetts) of Saturday 20^th June 1846:

Shooting one’s Grandmother.—The above is the English of a very common expression, that is used when one individual would laugh at another on account of some mistake that he may have made. It commonly falls upon the ear after this manner—that’s the time you shot your granny. With the origin or meaning of this queer expression we are wholly unacquainted, but the idea which it suggests to our mind, we will illustrate by the following story:
Once in the olden times, there lived in the goodly city of Cincinnati, a certain ancient gentleman, who was noted for his wealth and eccentricities. He had a beautiful daughter, the winning of whose heart was the chief ambition of all the young men in the country.—Among the many who had never been introduced, and therefore, only admired her in the abstract, were a couple of Kentucky bloods from Lexington. They were bosom companions, but as fate would have it, both striving for the same end, viz: an introduction to the fair unknown. They finally concluded however, that they should become acquainted at the same time, leaving the more distant future to the decrees of fortune.
In process of time they made their appearance in our city, but as they had brought no letters with them, and were unacquainted with the aristocracy, the commencement of their campaign was gloomy. For a few days their principal amusement was to walk by the mansion where resided the Buckeye ⁵ charmer, and this they did in the morning, at noon, and in the quiet evening of every day.
On an occasion it so happened that they chanced to walk within hailing distance of the old gardner of the mansion, who was busily engaged in trimming some grape vines, when the idea suddenly entered their noddles that they might employ his services to advantage. Whereupon they jumped over the fence and the elder of the two commenced the following dialogue:
“Halloo, old Covey, here is a silver dollar, and now we want you to give us a helping hand.”
“Well, gentlemen, I shall be happy to assist you; what is it you want?”
“We understand that your master has a very pretty daughter, and we want to become acquainted with her. We are strangers to the city, and would know how we may be introduced?”
“That’s rather a puzzling question young gentlemen. But hold! I’ll give you my advice. There is a gentleman living at the Broadway Hotel who is very intimate with the family, and if you will scrape acquaintance with him, I doubt not he will be happy to gratify your wishes.”
“Thank you, thank you old Covey, we stop at that Hotel, and the game is opening beautifully. Good afternoon, John.”
A couple of days passed away, during which time there had been certain manœuvres carried on which we will leave to the reader’s imagination, The young bloods succeeded in securing the co-operation of the family friend, whose noble conduct they were coustantly [sic] extolling to the skies. The hour for the long desired introduction finally arrived. With bows and smiles, and tender speeches, the Kentucky gentlemen were ushered into the splendidly furnished parlor of the unknown nabob. In a few moments the wealthy beauty made her appearance; the lady, who was in great glee received them in the most polite manner possible, and the lovers were perfectly mad with delight. The evening chat was exceedingly interesting to all concerned, but was interrupted by the following concluding scene. The lady who had left the room for a moment, presently made her appearance hanging upon the arm of an old gentleman, and as she approached the young Kentuckians, she tossed over a silver dollar to them, and begged permission to introduce to their acquaintance her father the old Covey, and gardner. Such is sometimes the end of even Kentucky chivalry, and one of the many mode [sic] in which people occasionally shoot their Grandmothers.—[Cincinnati Chron.

⁵ Since the early 19^th century, Buckeye has been used to designate a native of Ohio, in which the American horse-chestnut (Æsculus glabra) abounds.