I like to use 8mm snap blades from Dollar Tree. I also have some Exacto type blades as well.
For straight lines, I cut just the paper on the first swipe. Then, follow the cut with another swipe going through to the bottom paper.
For cutting outside curves, I don't try to cut the curve in one swipe. I will take several swipes and gradually shave it off.
For inside curves, I will cut only the top layer of paper. Then, punch through the cut with a pin to mark the cut location on the other side. Then flip the foam over and cut on the punched line. Only cut the paper. Then the foam will "snap out".
The same goes for cutting tab slots. Cut the paper on one side, mark the corners by punching a pin through, flip the foam and cut the slot at the pin marked locations. Now the paper is cut on both sides at the same location. Push the foam blank out of the slot.
I tried cutting slots all of the way through (from one side) when I first started building. They always ended up skewed.