The original meaning of 'hash' was a dish consisting of bits and pieces of meat cut up small and cooked with gravy etc. The earliest recorded version of the phrase 'settle someone's hash' dates back over 200 years, the idea behind it being that the meal...ie his fate...has been prepared and there's nothing he can do about it.
We see the same idea in the phrase "your goose is cooked". In other words, it cannot now be uncooked, in the same way as the hash cannot be re-treated and produced for the table in some different form. "You've 'ad it!" in other words.