ropes, cable, chains... tell ya know, do not make a running start (slack in chain) you will snap it all. and it will come flying back at you, and either kill you or sever something from your body.
if ya pulling with a rope/cable/chain, set tractor at an angle. so if rope/cable/chain does snap, hopefully it will snap straight out, and not angle at you.
and of course use shortest amount of chain possible between what ever ya trying to pull and tractor.
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backhoes are awesome, ya do not tear up entire tree at once, ya use the backhoe, to rip up the smaller roots underground. some of the roots may want to go soft on ya and not tear/rip apart. but that is how it is. if a root is to big, move backhoe over a couple feet, to tear up the smaller roots.
you will most likely push/pull the tree over a few times in different directions till ya get some experience in dealing with the roots. some times pushing it back and forth may be only way to get backhoe bucket onto a root and tear/rip it apart. it would be nice to have a hydraulic thumb, that was more likely a large machete blade to it for dealing with roots. but *shrugs* ya use what ya got and ability of the machine to tear up some roots.
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when it comes time to pulling the trees to were ever. take the 3pt backhoe off. and pull via draw bar. 3pt hitch backhoes are made to come off for a reason.
and like others have said, be ready for possibly flipping the tractor backwards onto itself if something snags and tires bite in (foot on a clutch or hand on a clutch, and brakes. again keep chains as short as possible. and never do a running start.