The word "joed" is a word I use frequently to describe my feeling tired or exhausted. As a child, I used to hear my grandfather say "I feel joed" before he would sit down for a respite or turn in; however, I'm not certain why the word joed means tired. Has anyone the least notion why "joed" means tired?
Much as I admire the Random House Dictionary of Historical Slang (cited in Grant Barrett's answer), its decision to list the slang verb jo in the sense of "spoil" (on the strength of one occurrence from circa 1800) in the same entry with joed in the sense of "tired, exhausted" from 1932 seems to me to be quite a stretch. I checked multiple dictionaries of American slang from the 1800s and early 1900s and didn't find any that cited either meaning of jo/joed. I consider it much more likely that joed in the "tired" sense emerged independently of jo in the "spoiled" sense.
The earliest instance of joed that I've been able to find in a slang dictionary is from Harold Wentworth & Stuart Flexner, Dictionary of American Slang (1960):
joed adj. Tired out. Not common.
Wentworth & Flexner doesn't suggest any source for the term, but it does provide two intriguing entries for a couple of nouns that may be related:
jo n. A shovel.
hemo-jo n. A shovel or spade; work done with a shovel, such as ditch-digging; hard manual labor.
So while the connection is by no means a sure thing, it seems possible at least that someone who spent a long day doing hemo-jo with his jo might come home feeling joed.
Another interesting usage, cited in Harold Wentworth, American Dialect Dictionary (1944) is this:
joe 1. v.i. To move slowly. 1927— W[est] V[irgini]a. "Joe along."
The earliest relevant instance of joed that a Google Books search finds is from Francis Mason, Pilots, Man Your Planes! (1944) [combined snippets]:
"It's not stuff," insisted the Flamingo flight captain heavily. "I'm sure of it—so sure that I've been writing letters." He nodded to a stack of envelopes on the rickety table in one corner of the room. "I'm joed out and—well, I won't mind."
"Cut it out, Hugh! " cried the visitor as the eerie quality of Steel's prediction gripped him. "Don't talk like a darned fool! You'll be flying years after the rest of us are pushing baby buggies back home ..."
Another instance appears in Felix Morley, Gumption Island: A Fantasy of Coexistence (1956) [combined snippets]:
"I'd a bin mos' too joed to git home, if Mr. Caselli hadn't fixed up this ride. He's always fair, but he sho' do push hard. A shovel's mighty heavy, when you ain't used to anything bigger than a fry pan."
This last example is especially interesting because it (unlike the 1944 example) explicitly involves work with a shovel.
This doesn't directly answer your question, but the Historical Dictionary of American Slang volume II has an entry:
jo v. 1. to spoil; (also) to exhaust. *ca*1800 in Dolph Sound Off! 503: As to Saratog' he came, thinking how to jo the game. 1932 AS VII (June) 333: Joed—tired; exhausted.
I'm not sure I agree that those citations are the same word, however, especially as the citation evidence is so sparse. AS is an American Speech article, which is about John Hopkins University language.