This is tried and tested by ourselves a while ago! Was so glad I'd read it somewhere.
A little bit of sugar on a spoon; works wonders. Let them lick it off or try to let it go where the cut is.
Whether it's the sweetness that distracts them or something in the sugar that coagulates the blood- or both - I'm not really fussed - the fact that it stopped the screaming and mouth of blood was enough for me!
(Bean was bobbing up and down in his cot and then smacked his mouth on the bar
so this was for small cuts from a tooth piercing the lip - not sure on a bigger cut though x)