As long as the rigging holds...
As for an anchor, you are craning out re-usable mass. You can choke or otherwise anchor to several logs on the ground, somewhat plumb below the tipped tree's connection (rope, chain, cable), to compensate for the released force (mass and leverage) of pieces being lifted off the tipped tree by the crane.
If you use a POW on the rope between your anchor and the tree, when the tree wants to flip back down into the root hole, you can control it, to a degree.
I can see it handling it both ways, and like so much, is situational dependent. What does the customer want to pay for, and what are your tools/ skills/ resources to match the job?
If you can rip the stump out, you have a crane to load it onto a dump truck/ trailer. RopeArmour/ Tommy has a video of cutting roots and using MA with dyneema rope to lever a tree over a fulcrum (a log) and ripping the whole spar and stump out. Hose it off, and cut off the log. Then, just dump soil.
If you don't have machines for loading, grinding makes the stump into human-sized pieces.
