drywalltools
I have a pile of drywall scrap that's been sitting in my garage for a few years after a remodel, "just in case". My buddy came up with the idea of turning it into "karate boards" for our kids to destroy. Scrap pieces start at half sheet (4×4) and go down.
I'm also on the lookout for an excuse to buy something new. (Honey, it's for the kids!) At this point my only idea is to use the circular saw and toss the blade afterwards.
In addition to the normal tools like pruners, hedge shears, etc., my tools for controlling unruly vegetation include:
In your situation, I would start by using these tools to cut back all the vines close to the ground. Dig as much of the roots out as possible, then keep an eye on the area for new shoots and dig them out (or spray them with weedkiller) as they pop up. Eventually you'll get rid of them, though it may take persistence on your part.
For thicker pieces you might find you get better results by compressing the foam before cutting it. You could make a simple straight-line clamp out of a couple of 2x4s linked with a door hinge -- just put your foam in between, clamp the open end shut with a C-clamp, and use one edge of the wood as a guide for your cut. For your curved cuts it might make more sense to make a plywood die to match the final shape and press it down by hand or with something heavy before cutting around it.
Best Answer
A craft knife or box cutter will do the job very quickly and cheaply. You only need to score the front side of the drywall and then it should snap cleanly enough along the score line.
If you already have a Dremel or Roto-Zip, you can get drywall bits for them that will make short work of any drywall.