No.It is not. It's the crime of criminal damage to property, the dog,and may be cruelty as well. The dog's owner could also sue in the civil court..
Exceptionally , a farmer is only allowed to shoot a dog which is physically 'worrying' his livestock at the time.That's because the dog can cause livestock to abort ,and cause other harm to them ,which causes loss to the farmer as well as suffering to his animals. So he can then shoot the dog in order to put a stop to or prevent immediate loss .Even a farmer cannot shoot a dog on his property simply because it is there
Incidentally the saying 'a man's best friend is his dog' comes from an old American case where a landowner did shoot a dog which strayed on to his land. The owner sued and , naturally,won.