How to get rid of grapevines?

I have really old grapevines. I've chopped them with a machete and cut off most of their lateral roots, but they keep putting out new growth from the big center stump.

Is it enough to chop their main stump 5-10 inches below ground level – will they die in a few years if I do this and keep pruning new growth?

Do I need and would it help to use a tripod hoist to pull the root out? they look kind of weak from previosly hacking them.