I have done this twice, and it IS work, but it works. We have sandy soil in
Nevada where these trees were planted. We started digging them out by the
roots, and used a big shop vac to remove the dirt as we went. This way, you
could easily see the roots that were holding the thing. We cut those with a
sharp double bladed long handled axe. Any type of chainsaw or regular saw
dulls quickly. On one, we had a come along on it with a tight bind on it
because we couldn't get the truck close. On the other, we had a chain to a
four wheel drive truck. It was slow going, but in both cases at a time once
it started to move, it popped out from there, breaking the remaining roots
on its own.
Don't know if that would work with the type of soil you have. We had a
neighbor who suggested the water blaster idea, but decided we would soon
have a muddy moat. It was a chore, but they took only about three hours
each. One was a eucalyptus tree, and the other a chinaball. Both trunks
were about sixteen inches in diameter. If you haven't cut the main trunk
yet, leave it a little tall, and this will improve your pulling leverage.
HTH. There is no easy way to do it.