What tool will allow me to make a cutout in the middle of a vertical sheet of cardboard

In addition to the normal tools like pruners, hedge shears, etc., my tools for controlling unruly vegetation include:

• pruning saw (look for one that cuts on both push and pull strokes):

• bypass lopper (much more leverage than a regular pruner):

• tree pruner (no more climbing on a ladder to get at high branches!):

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.

You could make some utility or razor blade holders from wood. Saw a rectanglular block down the length at the desired bevel angle, clean up with a hand plane, then clamp the blade in the centre using predrilled screws, from both sides.

You can then use it by drawing it against a fence, either plunging like the mat cutters or starting from the edge of the material.

It would be inexpensive to make a few standard angles; you could extend the range by placing thin shims along the part closest to the fence to achieve steeper intermediary angles.