At first I thought you wanted to keep it alive.
but since you just want it gone start digging
and cut through the roots with an axe
wash with the hose as you go so you can see where to chop it
it wont be as big as you might think and it will come out fairly easy by hand once you get the roots chopped
there will be a lot of small fiberous roots which you can just cut through with a sharp spade
leave the roots in the ground to rot

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