Is killing an animal sinful according to the Bible?

No, the Bible states that animals were placed on earth for man to use freely. If you want to kill a cow and eat it, or kill an insect because it's annoying you, the Bible says that that is perfectly fine. If you are talking about killing stray dogs for fun, that is a completely different thing. As long as you aren't doing it for violent, sociopathic reasons, it is alright according to the Bible.