Aggressive vines and grasses can be a real bear. Pull what you can and starve the rest out with black plastic. That's the only way I know to get rid of such things without chemicals.Oh, you'd be surprised... I have some type of thorny vine from hell that is quite aggressive. It has come up through a 3 ft bed that was loaded with wood chips. I eventually just moved the whole dang bed and gave up.
Do not attempt to till/cultivate aggressive vines or grasses to get rid of them as you will likely just redistribute them and increase the number of pants.