Help Needed: Keeping Cuts Vertical

When cutting parts that are laminated to thick cardboard or foam core, how does one keep the cut edges vertical? I swear I'm holding the knife completely vertical, but the cut edges are coming out angled. This is significantly worse when cutting circles as opposed to straight edges. And when the part is a former that will be glued edge-on to an outside piece, a flat edge is very important.

Attachment 256417

For straight cuts, I'm about 50/50 on getting it vertical, and if it's wrong, it tends to be an obtuse angle, like so:
Attachment 256418

For circular cuts, almost all of them are acute, like so:
Attachment 256419

This raises a more in-depth question, too - when cutting with a saw blade, the blade creates space for itself by removing material (i.e. a kerf). When cutting with a #11 or razor, there's no kerf; space for the blade has to be created by distorting the material. For thin materials, like paper or regular stock, this distortion is so minimal that it's not really noticed. But I suspect that it's this distortion that's causing my cuts to not end up vertical, and I know it can lead to damage to the material and thus rougher edges. How does one account for and address this problem?

I guess what I really need is a small jig or band saw. Or maybe rig a Dremel with a cutting bit?

Attached Images

	perfect.png (778 Bytes)
	obtuse.png (1,003 Bytes)
	acute.png (1,016 Bytes)