IMO, from reading the OP, I'd say that this is not the right home for the dog. I agree with a lot of what was said along those lines above. I mean, one bite to a human, fine; two bites, ok, it's a habit; but three bites? The dog is clearly not being managed well.
Incidently, the tie out thing is the very reason why there are more and more cities all the time writing legislation banning leaving dogs out on tie outs.
That said, my vote was for PTS, though an in-home trainer or behaviorist would also be a good option. The reason I didn't say rehome was that the right home for this dog would have to know a lot about dog behavior and really be able to handle a dog with issues like this. I can 90% guarantee you that you will not find a suitable owner who is willing to take on this dog. I know, because a rescue group I work with has a similar dog that they've been trying to rehome for 2 1/2 years, and they've pretty much given up and will keep him in the shelter permanently. (Luckily he seems happy in the shelter and does get along well with most of the staff.)
There are only a few types of homes that would be good for this dog:
A professional trainer. I am a professional trainer, and I can tell you that most of us get our share of "problem" dogs at work, and do not want to deal with another when we go home to relax. Plus, most trainers need demo dogs or performance dogs, and this dog would be neither.
Someone with a lot of dog experience though not a professional trainer (AKA a chazzer
): 99% of these people already have a dog; the remaining 1% probably don't have a dog because they can't have a dog. Plus, these people are probably also going to want a performance dog.
Someone with no other pets and no kids. People with no other pets are usually also less experienced with dogs, and will be less equipped - and less willing - to deal with this particular dog.
So yeah, it sounds simple to say the dog just needs the right home. But the fact is it's going to be so extremely difficult and time-consuming to find the right home, IMO it would be a better idea to have it PTS.