A lopper and heavy leather gloves. A lopper is essentially a large scissor or wire nip. Either bypass (scissor) or anvil (wire cutter). Available at a hardware store near you. Or Lowe's.

I have the same problem. Large weeds almost plants. I am pulliing them out one by one from the root. Wear good gloves and get to their root. If your weeds are on a path away from any other desirable plants you might want to try RoundUp type products, although these are quite strong weedicides mind you.

Removal of roots is far more advisable than simple cutting. Depending on the weed, many will regenerate promptly from residual roots systems. Loppers are good to remove thorny topgrowth down to a manageable size, but I'd try a 3-prong cultivator to loosen the soil around the roots and pull the remainder.

I am of the old school that considers manual removal of weeds preferrable whenever possible to any sort of chemical product.

Most weeds that assume a 5' height can be cut through at or below the crown and will not come back. We have a common pigweed variety that we call "careless weeds" that get that large. We control them by shoving a spade through the weed at ground level. We also have something called "ironweeds" that are too tough to kill with a spade, so they have to be dug out. On the farm where I grew up, weeds that couldn't be reached with a plow because they were in the crop row would have to be removed in this fashion before harvest, or they would get in harvest machinery.

Here is a link that might be useful: Pigweed