If you mean "Mule-Tied", the southern expression...
I believe it refers to being trapped in a bad situation by someone's stubborness or less specifically, just trapped in a bad situation. Similarly it can just mean "Stuck".
The imagry being referred to is a farmer etc. who has his mule tied to a tree... and somehow the mule walks around the tree several times while the farmer is close to the tree, tieing the farmer to the tree. Mules don't obey like horses, so it's hard to get them to follow commands, and basically the farmer would have to have a tug-of-war with the mule via the rope to pull the mule in close enough that he could guide it back around the tree until the rope was loose enough for him to slip out of.
It's an old cartoon image used a lot in the 1800s, though i'm not exactly sure if the phrase preceeded the Cartoons, which would be referring to them, or if perhaps the phrase grew from cartoonists use of the humor of the image, usually in politcal cartoons.
As well, in the southeast, it came to be used as an insult or barb in the 1900s, which i can attest to from the older members of my family... used in the manner of "You mule-tied fool!" or "Don't be such a mule-tied fool".
A saddle mule is a mule used for transportation or riding, were as a pack mule is a mule used solely for transporting luggage rather then people.
Mule Skinner
Mules are sterile, a mule is the offspring of a donkey and horse, therefore sterile. A male mule can mate with a female mule, but will never get her pregnant.
A male mule is always sterile, however , rarely, a female mule will be able to reproduce.
The answer to that question is a mule. The mule is used to pull carts, and used on farms. The mule cannot reproduce, it's genes are unbalanced. It has more horse gene combinations then donkey combo's.
mule = Maultier mule = Muli
A saddle mule is a mule used for transportation or riding, were as a pack mule is a mule used solely for transporting luggage rather then people.
Mule Skinner
mule = Maultier mule = Muli
A donkey can have offspring that is a mule, a mule cannot have offspring that is a donkey.
tête de mule (addressing the stubborn mule), têtu/têtue comme une mule (describing someone as stubborn as a mule) are standard French expressions.
mule
The name for a male mule is a Jack.
A mule is a cross between a horse and a donkey. A mule is sterile.
A molly (female) mule. The term for a male mule is 'mulet'.
Mules are sterile, a mule is the offspring of a donkey and horse, therefore sterile. A male mule can mate with a female mule, but will never get her pregnant.
The mule hauled my cart up the hill. The lady bought a mule for her "car". Do you know what a mule is? A mule is a weird but kind animal. (I think) Hope this helps! Peace out~Tj8rocks