^^^
You can and should punish them like a horse, but not for all the same reasons. You have to train a mule like you should train a horse. Nipping, kicking, wiggling, not listening, and all that deserve correction, but not if they are kicking, nipping, not listening, or wiggling for a good, mule sensible reason. Just like you should only punish a horse if he's disobeying you of simple disrespect rather than a good, sensible reason.
You say, "What is a good reason for a mule not to listen?" Imagine a trail ride. Suddenly, mule sees something and stops dead. You kick, but he's pulling a donkey on you and won't move.
First, why isn't he moving? Well, he's scared of the sound ahead. He's deciding if he should run, attack, or go on. A scary, possibly deathly sound is a good reason to stop in a mule's mind. He's just thinking; don't hit him for it. If you give him time to think, he'll sort it out on his own and never be afraid of that sound again.
Some situations that do require "punishment" require special care when working with mules. Imagine one day you're about to saddle up your mule. You've had your mule for years and years, but one day he's decided that he doesn't want that bit in his mouth. First, examine for mule sensible reasons. Is the bit hurting him? No. Have you recently changed bits and he doesn't like this one? No.
He's playing games with you; testing you. But, in order to play games, you have to have two players. If you get mad, mule wins. If you give up, mule wins. But if you keep going like nothing's happening until you get that bit into his mouth, you win. Hitting doesn't help; simple patience will work for most mule misbehavior's. (Except biting and kicking for no reason. Slap the heck out of 'em! Never but up with aggression!)
That grand trick to training mules is to find out why they're doing something rather than fixing what they're doing.
EDIT: Dang! I went out on a tangent! Sorry, everyone! I like to talk about mules...
