First, the quote from the letter that set me off, which is also the earliest web reference I found to "garden sauce" (note all bold emphasis in the following quotes is mine):
Owing to the great emigration into this place, provisions are high and we shall have to pinch a little perhaps till we can raise them ourselves, shall immediately plant some potatoes, garden sauce, and sow some turnips; and calculate to put in some wheat, and plow as much as possible for spring crops...from letter by Ezra Maynard, June 4, 1824.
In 1852, Brigham Young preached the following:
Here are their gardens groaning with abundance of the products of the earth — with potatoes, beets, and cabbage. Here are milk and butter and fine flour in great quantities. Here are the tomatoes and garden vegetables of every description. Now, you say, I have got home, to my brethren’s door, and they have got plenty. What would you wish these brethren to do to you? Ask that same question to your neighbours, and get them to answer it. I can tell you what you would they should do to you. You would wish them to say, Come, brother or sister, into my garden, and help yourselves to some garden sauce; walk in here, and take and eat, and make yourselves glad.
From a letter from a Civil War soldier in the South in 1863:
Very few Southerners ever eat any beans. We have also plenty of garden sauce, cucumbers, beets, etc. and in the streets can get huckleberries, blackberries, apples, pears, peaches, etc.
I found the intriguing title "The Balloon and the Garden-Sauce" on a poem published in 1889 by Irving Browne, but although The Green Bag (an Entertaining Journal of Law!?) is still being published, I haven't searched out the 19th c. issues in any library archives. From these quotes, though, it appears obvious that garden sauce was a term for what we would today call produce: vegetables, grown in a garden, in contrast to grain, grown in fields.
I did not find an explanation of the origins of the term "garden sauce", but did uncover the the following citation from Betty Crocker’s Picture Cook Book, ca. 1956:
In the early days of our own country, vegetables were "garden sauce" or just "sass" to go with meat. Beets and carrots sometimes were referred to as "long sauce", while onions and potatoes were "short sauce". A vendor who sold vegetables from door to door was a "sauce man".
Ah ha! Garden sauce at some point in the early 1900's became "garden sass". A column on “Sauces to Impart Richness”, by Catherine Mackenzie in the June 30, 1935 edition of the New York Times (p.SM12) also describes how:
"...the return of the gardening season serves to recall that vegetables were long known colloquially as "garden sass," and a vegetable garden as a "sauce garden". The Oxford dictionary defines one use of the word “sauce”: “Chiefly US, vegetables or fruit, fresh or preserved, taken as part of a meal or as a relish”.
When you search the web for "garden sass", more interesting citations turn up, including at least three books with the title "Garden Sass" published since 1950; one subtitled “A Catalog of Arkansas Folkways”, another “A Collection of Recipes by the Growing Season”, and the final one “The Story of Vegetables”. It is also clear that sauce is something that accompanies meat, and that at least in the early 20th century, garden sass was not as valuable as meat, or of much account in general. This become more obvious in the following quotes:
He was a little and dried-up man of something like 80 years. Mounted like a manikin on the back of a big white horse, he bore before him a bunch of green corn-fodder, and turned in at the gate to a piece of low ground thick with walnut-trees, between the rows of which the soil was studded closely with that peculiar greenery which delights the peasant soul, and which, when finally realized upon, does not amount to any value whatever; pumpkins and peppers and onions, some spindling stalks of corn for roasting-ears, and all that miscellany which comes under the comprehensive head of "garden-sass," and which, so far as all modern experience goes, it is cheaper to buy than to raise...from Old Californian Days, by James Steele, 1889:164-165
Thirty dollars for tools and seeds, ninety-seven dollars' worth of labor, and four times that amount of worry and vexation of spirit, results in some forty dollars' worth of "garden sass," which is promptly referred to the interior department of the neighbors' cows...from "The Cow", in The Iconoclast, by William Cowper Brann, 1898
At this moment Case pere and mere emerged from the kitchen loaded with provender. "Here`s enough an` more`n enough, I reckon," said Jeb Case. "We got eggs, butter, bread, bacon, milk, an` a mite o` garden sass."
"But we ain`t goin` to charge you nothin` fer the garden sass," interjected Mrs. Case...from The Oakdale Affair, by Edgar Rice Burroughs, 1937, ch. 7.
Today "garden sass" is a quaint phrase, a mention of the Good Old Days found only in historic documents. It also appears to be something you might name a blog or an art exhibit, as in Love Apples and Other Garden Sass, a interdisciplinary show in Brooklyn, where "All the artists in the show individually contribute their ongoing correction of personnel mythologies and unraveling stories, like a garden sass casserole."