If your dog continues to snap or growl, seek a professional dog trainer for advice and help.
Many hunting skills are instinctive for the dog. Instead, work on teaching your dog to respond to your voice and come when called.
Parson Russell Terriers (formerly known as Jack Russell) are small hunting dogs. The Jack Russell Terrier was bred to hunt and dig (go to ground) for rodents and other small animals such as squirrels by treeing them. Parson Russell Mixes tend to be small, between 10 and 14 inches tall at the withers. They are usually mixed with other terriers; other breeds that are strong-willed and will misbehave without careful training. The key to training a Parson Russell mix is to exert your dominance as the leader of the pack.
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Begin training early. Start the training process the day you bring your puppy home. Parson Russell terriers are usually intelligent but can be domineering. You must assert your own dominance early.
Use positive reinforcement. Praise and give loving attention when your dog behaves properly. Ignore the puppy when he misbehaves. Don't punish a Parson Russell mix. When they feel threatened, they assert their dominance.
Be consistent. Don't allow behavior one time and punish that same behavior the next day. The dog becomes confused and doesn't understand your expectations. The Parson Russell and Parson Russell mix are usually quite intelligent. They are hunting dogs that have been bred to solve problems to catch prey. If the dog remembers getting away with bad behavior even once, she will try it again.
Socialize your dog early. Unlike herding breeds that work as a pack, Parson Russells compete with other dogs for prey. Socializing a young puppy helps override this instinctive behavior. Take the puppy to obedience classes, agility trials, Rally O or the local dog park. Praise him when he behaves politely. Separate the dog, but ignore snapping or growling.
Teach your puppy good manners in the house. As your puppy matures, he may try to assert dominance. You can't allow the dog to get away with bad behavior, even when you are tired and feel like giving in. Do not allow a puppy to sleep with you if there is any growling or snapping; your dog is trying to exert dominance over you. Instead, remove the dog and crate him for several nights. Do not allow him on the couch until you are sure he will reliably relinquish his position without a fight.