The term sad sack denotes an inept blundering person.

It originated:
– in U.S. Army slang,
– in the early 1940s,
– according to its earliest definitions, as an epithet for a dejected or sloppy soldier.
—Cf. the name Joe Soap, which originally designated an unintelligent person in British Army slang.

In Green’s Dictionary of Slang, the English lexicographer Jonathon Green (born 1948) indicates that this term is an abbreviation of sad sack of shit, of same meaning.

The American cartoonist George Baker (1915-75) popularised [see footnote] the term in the cartoon strip:
– titled The Sad Sack,
– depicting the misfortunes of an inept private in the U.S. Army,
– published from 17^th June 1942 onwards in Yank: The Army Newspaper (H.Q. Detachment, Special Service War Department – New York).

The following is the first cartoon strip titled The Sad Sack, published in Yank: The Army Newspaper of 17^th June 1942, in which the newly-recruited private undergoes the physical:

The earliest instance of sad sack that I have found is from the Bergen Evening Record (Hackensack, New Jersey) of 17^th August 1942:

Soldier Slang

The antiaircraftsmen assigned to duty in the neighborhood have an uncanny genius for not calling attention to themselves, but it ought to be observed that they’re making some quiet alterations in the language as you’ll speak it. Since soldier slang has a way of sticking, can this department claim a first in the formal recording of these?
SAD SACK, n.—A sloppy soldier; the possessor of an important hangover; a born basic (q.v.); a Benny (q.v.). Civilian equivalent: a drip, a jerk.
BORN BASIC, n.—A soldier whose inherited mental equipment dooms him to a career of menial duty, forbids promotion.
BENNY, n.—(probably from Corporal Henry McAlear’s crackerjack cartoon “Benny the Bungler” in the Eastern Defense Command’s weekly “America’s Alertmen”)—A lout; a stupid, generally loudmouthed, slovenly born basic. It is an epithet applied to soldiers who talk too much.
SPOON UP, v.—To curry favor in unworthy ways; to grovel before officers. “See that Benny talking to the blonde on the corner? Around the battery area he’s been spooning up all week for this furlough.” College equivalent: apple-polishing.
The idiom as to “8-ball” has undergone an Army change. Originally and correctly a derivation from a variety of pool, meaning in the phrase “behind the 8-ball” something like hoodooed or in the soup, it come [sic] out like this:
“A lousy 8-ball like the guy that just went past with his cap on the back of his head does more to hurt the Army than 10 of us can do to help.”
“Hey, don’t you know better than to talk to these civilian 8-balls in a saloon?”
In this usage the term retains its original supernatural flavor. The 8-ball is bad medicine, ominous, as well as just unpleasant.

The second-earliest occurrence of sad sack that I have found is from The Casper Tribune-Herald (Casper, Wyoming) of 18^th October 1942:

‘China Clipper’ Doesn’t Fly—Not Even at an Air Base—in Soldier Jargon

As different as the clothes he wears and his new surroundings is the jargon that the Army recruit finds his fellow enlisted men speaking.
The old bromide, “the Greeks had a word for it,” might easily be modified to say, “the American soldier had a word for it.” There is hardly a sentence spoken during his off-duty hours that doesn’t contain some phrase or word in his army vocabulary.
Where anr [sic] when many of the words and phrases originated is not known. Some were coined during World War I; others are products of the “new army.” A new phrase or word, originated in one army camp is certain to “catch on” at all the others.
Most of the words are inspired by the army mess hall: “chow” is food; a “chowhound” is one who over-eats; “china clipper” is a mechanical dishwasher; “french-fried mothballs” is hominy; “G. I. (government issue) lemonade” is water; “sand” is salt; “cat beer” is milk; “swamp seed” is rice; “kennel rations” is meat loaf; “irish grapes” are potatoes; a “belly robber” or “slum burner” is a cook.
It isn’t unusual for a soldier to compose an entire sentence of army jargon. For instance he may say, “Instead of sweating out the chow line, I’m going to do some horizontal blanket drill.” Translated, it simply means he isn’t going to wait in line to eat, but he’s going to take a nap.
A few of the other more common words in the soldiers vocabulary are “sad sack,” a dejected or sloppy soldier; “goldbrick,” a loafer; “yardbird,” one assigned to menial tasks; “topkick,” a first sergeant; “N. C. O.,” a non-commissioned officer; “G. I.,” anything which the government issues (may also apply to a short haircut); “chili bowl,” a short haircut; “eagle,” a dollar; “the eagle flies,” means it’s payday; “sugar report,” a letter from the sweetheart; “dragging your feet,” relaxing; “go over the hill,” to be absent without leave; “dog robber,” an orderly; “jawbone,” something temporary or purchased on credit; “mit-happy,” adjective to describe one who salutes unnecessarily; “eager beaver,” one who does more than his share of the work; “jackpot,” a neophyte pilot; and “eggs,” bombs.

The following glossary was published in the Albuquerque Journal (Albuquerque, New Mexico) of 18^th October 1942:

From a Soldier’s Dictionary
Compiled by Corporal Richard Gaige

Ace in the hole: Alibi
Admirals: Medical Orderlies
Animal: Jerk
Apple polisher: Favor seeker
B. B.: Tough Sarge
Band beaters: Shirkers
Battle wagon: Fat guy
Black dog: One who has it soft
Bucking: Trying to win approval
Bullets: Beans
Butcher: Barber
Butts on that: Next after you
China clipper: Mechanical dishwasher
Choppin’-up: Hair cut
Clam up: Shut up
Colonel: Over-zealous non-com
Cook with both burners: Do your best
Cook with the front burner: To take it easy but keep going
Cookie: Girl
Cooler: Short hair cut
Crowdin’: Picking a fight
Cruiser: Soldier who doesn’t know much
Duck: Cigarette butt
Eyes wide open: Fried eggs, sunny side up
Fried crow: Chicken
From wood: Fake
Georgia ice cream: Hominy grits
Gig: Punishment
Goldbricker: Soldier who shirks work
Graybar Hotel: Guardhouse or jail
Grease trap: Kisser
Handcuffed volunteer: Selective Service man
Heap: Car
Hollywood private: Acting corporal
Honey wagon: Garbage truck
Horizontals: Habitual bunk fatiguers
Jail bait: Girl under age
Jaw boning: To borrow on credit
Muff the duck: Sneak away
Ninety-day wonder: O. T. C. graduate
Off and on: Off your tail and on your feet
Old Bess: Truck
Old lady: Mop
Rabbit food: Herb used as a salad
Rangooned: Shipped out in a hurry
Red-lighted: Scratched from a list
Republican: Any citizen
Root man: Permanent party
Sad sack: Someone in the dumps
Section eighter: Mental case
Shapin’: Coming along, showing Improvement
Shoulder pads: Griddle cakes
Side arms: Sugar and cream, salt and pepper
Skup the duck: Gold brick
Sparrow: Aviation cadet
Sugar report: Love letter
Sweepings: Hash
Taxpayers: Civilians
Throw him a high ball: Salute an officer
Torpedoes: Frankfurters
Ulcer Gulch: Kitchen in mess hall
Yard birds: Rookies

Note: The Oxford English Dictionary (3^rd edition, 2008) says that sad sack was coined by George Baker as the title of his cartoon strip—probably because the earliest occurrence of sad sack that this dictionary has recorded dates from 28^th December 1943, a year and a half after Baker’s first cartoon.
However, sad sack was more likely popularised than invented by George Baker, since it appears in a glossary of soldiers’ slang as early as 17^th August 1942 and without reference to Baker’s cartoons.
It is often said that George Baker declared that the title of his cartoon strip was taken from a “longer phrase, of a derogatory nature”. Unfortunately, this quote is never sourced, and is nowhere to be found in the documents that are available online.