When Hyakkimaru was born, he had no limbs, no tongue, no nose, no eyes, no ears and no internal organs. How could he possibly survive then? If he couldn't breath and he couldn't eat since he didn't have a stomach or lungs, does that mean that during the duration of his ordeal he was also immortal?
I don't remember the missing organs bit, but he isn't immortal. I believe both the midwife and the doctor said that Hyakkimaru had a strong desire to live. In other words, he's running on sheer willpower.