Perhaps more than most breeds, an improperly socialized dachshund is more likely than not to develop a habit of fear biting that can make interacting with new people or dogs something to fear rather than look forward to. Often, owners don't even realize why their dog is so seemingly aggressive just before running away or rolling over in submission. It may very well be that your dog is in a constant state of high anxiety.
For starters, the best thing you can do is make sure your dachshund puppy is well socialized as early as possible. You can do this simply by taking your new dog around. Making it a point to keep the small dog from being dominated while not coddling it is important. They are small dogs and an early attack can be traumatic.
Of course, all dogs, even in the same breed, are different. Some dachshund puppies (often runts) are just naturally fearful, though it usually takes some event to drive that fear home. Breeders can diminish this tendency by paying very careful attention to the puppies in the first few weeks after they're born rather than keeping the smallest pups away from the others.
To determine if your dachshund is actually biting out of fear rather than aggression, check to see how their ears are placed when attacking. If the ears are pinned back along the head rather than forward, especially if the dog is normally submissive around dogs he or she knows well, the odds are pretty good you have a fear biter.
Such dogs are often found at shelters and have been the victims of abuse. Just in case there is a genetic component to this, most professionals recommend one of the first things you do is get such a dog altered immediately, as they should not be bred. They certainly won't be making it into the championship ring.
The road for a dachshund that engages in fear biting is long and hard, requiring a great deal of patience and understanding on the part of the owner. Shouting at such an animal, often because they also tend to exhibit other behavioural problems such as submissive urination and an even more complete disregard of the orders you do give than is usual, even for dachshunds.
It's not easy to build the confidence of a creature that has a limited understanding of language, and dachshunds are even more stubborn that most breeds of dog about changing their opinions of anything. It doesn't suit their wild cousins to engage in rule changing once they've learned the ropes.
So, the trick is to find out what sets them off. Remember that all animals, even dogs are very sight oriented, though since their vision is different than ours, they key in to very specific things such as people with hats or flapping kerchiefs. You certainly should make an effort to never, ever loose your temper with the dog - it will only make things worse, no matter who terrible they're behaving. Surely there's a subtle way for you to let them know how displeased you are.
Families with dachshunds who are unable to deal with dogs that engage in fear biting would do better to contact dachshund rescue rather than sending their dog to the pound, as that's almost certainly a death sentence in most cities. What they need is understanding.