Try not to use a plastic straight-edge (although I do it quite a lot

). Use a metal ruler wherever possible and, preferably, two metal rulers with the foamcore sandwich-clamped between them. Doesn't have to be crushingly tight, just very firm.
Keep replacing your blades because they blunt very quickly on foamcore and make a ragged cut. Any resistance then gets your cut veering off.
Do not skimp on your blade quality. Cheap cutters are shite. There are many many particular scalpel blade shapes available for specific jobs. Yes, they can be expensive but waste far less material. And you're already saving money by going DIY.