So I got all the roots I could see on the first one but even having cut through all of them it would not budge.
Key words there are "I could see". Quite thin roots can be covered in soil and essentially invisible but still be enough to hold it in place.
The first time I dug out two tree stumps I, foolishly, cut them off low down and then started digging. The first, smaller, one was hard but I got it out after c. an hour. The second one I spent much longer, scraping away soil and cutting loads of roots before it would move at all. Then I could see more roots, so I kept on cutting, but when I had cut everything
I could see it still would not come out.
Eventually I put a piece of wood under the centre and the car jack on that, and gradually cranked it up. Two small 'explosions' later it was free and I saw that the roots that had been holding it were thinner than my little finger.
Do all roots go out sideways? Seems impossible to get to the ones underneath
It depends upon the specie of tree and the ground conditions, but there will always be some underneath and some trees have a main tap-root.
Cut everything you can find at the sides and what you can get at underneath, then try and lever it to one side and see what other roots are exposed. Do that levering it in all directions and you should gradually be able to get at all the roots.
A mattock is good for levering the stump, as well as for breaking roots. Depending upon the size, you may need a mate to lever the stump while you cut roots, or vice versa.
