Is it something to do with the fact that we're usually in a hot shower or bath while we're shaving, and our blood is nearer to the surface of our skin when we're warm, so it flows easier and quicker?? Ok, so not really an answer there, more of a question again!I'm hoping that someone else will reply and confirm/correct me.... sorry Jillybean no help at all! :oS
Im assuming its because the cut isnt deep enough to cut a nerve, so the nerve is sending a message to your brain saying that the skin that the nerve is in charge of is damaged and needs repairing?!?!?!?!?!?!?! Incase you havent noticed, i havent got any degree in biology!
As with paper cuts, it is cos you haven't cut deep enough to damage the nerve. So the underlying nerve is still sending the pain message to your brain. It's the same reason why deep cuts often don't hurt at all, you have severed the nerves.
It bleeds more because your leg is pointing downwards and the blood flows faster. Try elevating the limb for a few mins and putting light pressure on the wound and it should stop :-)