rotary cutter first (bush hog = lamen terms and a brand name)
then maybe a box blade with scraficier teeth down, to mess up the roots,
a potatoe plow / middle buster might work with deeper action that what scraficer teeth on a box blade would give.
mini ex (mini excavator) with more than likely a toothed bucket, would dig up a lot quickly. but still most likely want to mow it down before hand.
the mowing down before hand reasoning is that, all the vines even the roots will cause what ever you using to skid along top of the vines or roots possibly vs actually digging down into the dirt. mowing it down chops it all up. so stuff is more likely to pile up, vs getting caught up under cutting edge, and causing cutting edge to slide along top of it.