Interesting discussion. I seem to be suffering from skin "breakouts" more often these days and, when I do get a cut, it can be an absolute bastard to stop.
The thing about proper razor blades is that they are so sharp that you often don't even feel the cut; the first sign of it is a red bloom on your chin. Then, of course, because the blade has cut the tiny blood vessels so cleanly, clotting cannot take place easily and it can bleed for ages.
I've noted the above comments on the use of styptic pencils etc but I've tried almost all of the "blood stopping" products (there are only a few of them, compared to soaps or blades) and none of them are any good for anything other than a very minor bleeder. Styptic pencils (both those in the black holders and the long job in the plastic tube), Pro Raso gel, styptic matches (two brands) - none of them work on anything other than a very minor cut.
To avoid staining my shirts, I've invested in a few of those small, circular plasters - the ones that you get in an assorted pack that you wonder what on earth they are for because they are so small - and they are ideal for shaving cuts. At least they contain the bleeding until clotting starts.