When all the training recruits are in the throwing range, and the drill instructor Zim throws a knife at Ace's hand, when he first throws it, there is no blood. About 2 seconds later, there is a long trail of blood. This trail of blood does not get any bigger as Zim says, "The enemy cannot push a button, if you disable his hand."
Actually, after a couple of seconds, the human flesh wraps around the blade, so the bleeding stops. That also makes a knife/sword hard to take out once it's been shoved into someone, and that's why some old swords had that inset going trough their length, called a blood line, so that the blood keeps coming out of it (making more damage), and making it easier to take out from an enemy.
what you said about "blood lines" is a myth. Anyway, they're called "blood grooves", but that's irrelevant. They're actually called "fullers", and are only used to reduce the weight of the blade without making the blade much weaker. I've talked to quite a few bladesmiths and medieval arms experts about this, (as I thought the same thing you did, at first) and the ones who didn't just laugh at me explained it as I just did. This is similar to the whole myth about blades with triangular cross-sections causing "suck wounds" that don't close. They can be a bit harder to stitch, but they close just the same as any other wound.
The rest of it, about the flesh closing around the blade, though, is absolutely true. This is why you learn in first aid classes (and stage fighting classes) NOT to remove the blade if someone is stabbed. You bleed a lot at first, but it closes up quickly and almost no blood spills afterward, if you leave it in.