Used in association with the verb see, the humorous phrases said the blind man and as the blind man said pun on this verb’s:
– primary meaning, i.e., to perceive with the eyes
and
– secondary meanings, in particular: to understand, to find out, to examine.

These are the earliest occurrences of the phrases that I have found, presented in chronological order:

1-: From the Vermont Watchman and State Gazette (Montpelier, Vermont) of Tuesday 30^th March 1830:

Monday—I arrived in this wooden, mountain-hedged town to-day, and I begin to see, as the blind man said, that the people and place will furnish novelties enough to employ the observations of a foreigner, like myself, several days.

2-: From The Judge and the Freebooter. A Border Tale, an unsigned short story set in Jedburgh, Roxburghshire, Scotland, published in The Lady’s Book (Philadelphia: L. A. Godey & Co.) of August 1832—in the following passage, the jailer, Gustygowl, talks to his prisoner, Willie Armstrong o’ Gilnockie:

“Ye’ll be hanged, for as bauld as ye look,” said Gustygowl.
“We’ll see, as the blind man said,” responded Gilnockie.

3-: From the following paragraph, published in The Sun (Baltimore, Maryland) of Wednesday 27^th February 1839:

The Weather.—Of all the days in the year, yesterday was one most fitted to induce a poor fellow afflicted with the “blues,” ¹ to shove off this mortal coil. ² Cold, dreary, drizzly and rainy, it was calculated in an eminent degree to produce that careless indifference to every thing around you, coupled with the unconquerable disposition to give “the cold shoulder,” ³ to every man you met, and the undefinable desire to do a deed of foolish daring, yclept the “horrors”—yea, the “double-breasted horrors.” After a week of weather almost unexampled for pleasantness, yesterday was indeed a damper. We were amused at the soliloquy of one of the tribe loafer, whom we discovered shivering to the windward of a pillar in the Centre Market. “I’m blowed,” said he, “if I aint wet and dry both. The wet I can get over, and besides, it aint so bad considerin my clothes gets a washin; but the dry—there I’m a goner; I aint got a fip ⁴ nohow, and people always tells me they don’t go on the credit system. People don’t drop fips in the market now-a-days like they used to was. I hunted all this morning and did’nt find even a fip.—Times must be hard, that’s a fact, when people whats got ’em, can’t afford to lose ’em. Whew, but its cold, and it rains so everlasting hard—if there should happen to be a shillin in the gutter, the mud will kiver it all over. Its shockin hard ’lection so far off—if it was closer, I could borrow. Lets see, as the blind man said,—that’s a good one, by jolly—lets see if I can’t come it on some politicianer,” and he espied us; we decamped and left him in his glory.
P. S.—Nine o’clock, P. M. We have heard of no suicides yet.

¹ cf. the long history of the word ‘blues’
² cf. a Shakespearean phrase: ‘this mortal coil’
³ cf. meaning and origin of the phrase ‘the cold shoulder’
⁴ fip: short for fipenny bit, i.e., fivepenny bit

4-: From one of the unconnected paragraphs making up two columns on the second page of The Louisville Daily Journal (Louisville, Kentucky) of Monday 15^th June 1840:

Let us take an honest view of partiess [sic]” says the Globe. “Let’s see,” said the blind man.

5-: From The True Sportsman’s Gazette, edited by ‘Vates’, published in The Era (London, England) of Sunday 1^st May 1842:

The betting was so slight and ineffective as scarcely to merit notice. 6 and 7 to 4 was accepted about Eliza for the Two Thousand Guineas Stake, and Soult took the lead for the Chester Cup, as little as 6 to 1 being taken about him for this exciting race; Jolly Tar was in force at 12 and 14 to 1, both prices being laid, and Alice Hawthorn looked vastly like a drug ⁵, whilst the very name of Lanercost even did not greet the ear, amid rumors of tender feet, dry ground, and the “good thing” of the Marshal: “we shall see,” as the blind man said, and hear too, should we be within a mile of the judge’s chair on Tuesday.

⁵ I have not found out what drug means here.

6-: From the beginning of an article on the forthcoming U.S. elections, published in The Daily Madisonian (Washington, D.C.) of Saturday 15^th October 1842:

From the N. Y. Standard.
Let us see, said the blind man: let us see, for I fear some of us had a mist before our eyes, a delusion or spell, which is about to be dissipated.

7-: From Dramatic Mems, published in the Saturday Courier (Philadelphia, Pennsylvania) of Saturday 22^nd August 1846:

A Second “Power ⁶.”—The New York critics have gone into ecstacies over the debut, at the Park, of a Mr. Collins, from Dublin, on whom, they say, the mantle of Powers has fallen. Nous verrons ⁷. “We shall see,” as the blind man said.

⁶ The Irish actor Tyrone Power (1797-1841) had achieved international prominence.
⁷ French nous verrons means we shall see.

Published in the Public Ledger (Philadelphia, Pennsylvania) of Tuesday 8^th April 1851, the following advertisement uses the phrase to pun on the two possible meanings of blind man, i.e., an unsighted man and a maker/seller of window-screens:

LET ME SEE, SAID THE BLIND MAN, AND SO SAY I.—Let me see all my old friends, and new ones also, that are in want of a good set of VENITIAN BLINDS If any inquire for me, direct them to the HOLE IN THE WALL, 86 SECOND Street, two doors above Walnut, next to the Old Coffee House.
ap3 6t*32          C. W. CLARK.