Where did “Dipped in sh*t” originate from? What does it mean?

Solution 1:

"I'll be dipped," or the less polite "I'll be dipped in shit," meaning "I'm surprised," is most likely from the American South. One commentator, Sadie Smith, gives her personal experience in the Paris Review ("I Swear"):

It was then that he’d reach for the worst epithet of all: “I’ll be dipped.”

“I’ll be dipped”—said with a vehement emphasis on the last word that hinted at incipient violence, and with an Arkansas accent—was all the scarier because we weren’t sure what it meant. Sheep dip? Boiling oil? As a grown-up, I’ve heard it since in the South (or in its cruder form, “I’ll be dipped in shit!”) but it’s always a benign expression of surprise. Never does it convey the menace that my grandfather’s version did.

There are other reported variations. In Offense to Others (1984), Joel Feinberg compares it to "I'll be damned":

"I'll be damned" is very shopworn indeed, though it is still more effective than "I am surprised"; much better still is "I'll be dipped in a bucket of shit!"

Green's Dictionary of Slang has a first citation from 1961:

1961 G.L. Coon Meanwhile, Back at the Front (1962) 10: I'll be dipped in shit. I'll be the only man in history got a Purple Heart on the way to a whorehouse.

Given the context, it sounds like an Americanism that could date back to military use during the World Wars, and especially soldiers' creative capacity for colorful cussing.