To be honest I've never cut my self while on any drug (not that I can remember) but drugs tend to affect arteries and blood cells. Some of them cause vasoconstriction (constrict arteries, veins and blood cells) like LSD, MDMA, Amphetamines etc and that's the reason you might look pale on them and others cause vasodilation (dilates arteries, veins and blood cells) like weed causing red eyes. So my guess is that if you are on some drug that causes vasoconstriction and you cut yourself you will lose less blood (let's not forget that human body produce and release vasoconstrictors when you cut yourself), the oposite would happen if you have taken a drug that causes vasodilation.
If however you mean if your blood looks different when you are on drugs I highly doubt it, unless you tripping haha
