adverbs - "What do you care?"

  "I'm leaving anyway."
  "What the hell are you talking about?"
  I can't answer. I can't tell him that not only have I disgraced myself beyond belief or redemption, but I have also failed at my first opportunity to have sex-something I've thought about pretty much constantly for the last eight years. Not to mention throwing up on one of the women who was offering and then passing out and having somebody shave my balls and paint my face and stuff me into a trunk. Although he must know at least parts of it, since he knew where to find me this morning. Perhaps he was even involved in the festivities.
  "Don't be a pussy," he says. "You want to end up walking the tracks like those poor bums out there? Now get on out there before you get yourself fired."
  I remain inert.
  "I said get up!"

  “What do you care?” I grumble. “And stop shouting. My head hurts.”
(Sara Gruen, Water for Elephants)

In the example care seems to be an intransitive verb, and what has the role of adverb as an explanation below.

— adv 4. in what respect? to what degree?: what do you care? (dictionary.reference.com)

Then is OP the same as why do you care?

Answer

Although what do you care and why do you care have similar meanings, they have almost opposite uses.

Why do you care? is employed as a real question: someone is concerned about something which seems innocent or trivial to you, and you ask for a reason. It is ordinarily spoken with emphasis on why and care (but see snailboat's comment, below).

What do you care? is employed dismissively: it implies that the concern 'you' express is not something which touches 'you', and therefore 'you' should not meddle in the matter. It is spoken with emphasis on you.