Although service animals are supposed to be carefully tested for their ability to handle stress (called a temperament test) and should have very steady nerves, ALL animals, no matter how well-behaved, are capable of biting if pushed too hard. However, a temperamentally appropriate dog for service work will not respond violently to the owner being yelled at or the dog being stepped upon or bumped. These are things that can be expected to happen to a service dog during his working life. Yelping, or pulling away from a source of pain, such as being stepped upon, would be an acceptable response, but snapping (ie no physical contact), nipping (light physical contact), or biting would not.
Provocation of a temperamentally appropriate dog for service work would have to be extreme, such as violently striking the handler. A dog that bites with less provocation is probably not temperamentally suited for service work. Any service dog that bites for any reason, including extreme provocation, should be evaluated by a qualified behaviorist before returning to public access work.
In the US, the ADA permits the exclusion from public accommodations of any dog that behaves in a dangerous or threatening manner, and this would certainly include biting, or threatening to bite.