As I alluded to a few pages back: Super speed functions like a magical effect. I don't know if it actually IS arcane in nature, but it definitely operates conceptually instead of physically.
You aren't really so much moving your body faster than humanly possible as you are taking it, your clothing, and whatever you're carrying that you choose to bring with you into a different time stream. And "choose" is very much an operative word here, because the ground the speedster is standing on doesn't come along, and only the air necessary for breathing does while the rest of it acts like it isn't even there. The slipstream idea isn't really even necessary, and we've got plenty of examples of speedsters carrying objects in their hands instead of on their backs.
The F=ma violations suggest that, from within this alternate time stream, it's more like the rest of the world is moving really slowly than the speedster is moving really fast. Things like punches and pushes only affect objects in normal time with the same force they would have if the speedster was going normal speed.
If this theory is correct, then a knife wielded by a speedster would only be able to cut through the same things that the speedster could cut through at rest, with the super speed not contributing any benefit to the effectiveness.