Are you cutting the parts out of similarly small pieces of MDF to start with?

I've found one of the easiest ways is simply to put a screw in two opposing corners of the piece and hold it on to a larger sheet that makes for easy clamping.

If you are simply cutting small parts out of a larger sheet you can leave a very thin amount of material behind on the final cut so it is held in sort of like an air-fix model and you just need to cut the part out with a knife and neaten the edge up with a quick sand.