Amputations typically don't bleed that much. If completing severed the veins constrict and close themselves off.
You mean arteries. Yes, the arteries will often spasm and minimize bleeding. It's actually pretty cool to see. Repairing an injury like that is very difficult, as it's a "distraction" injury that pulls/rips the vessels longways until they tear, often shredding them. "Simple" chop or cut injuries are usually much easier.
And for all the guys who were having trouble with the left/right issue and making a left hand look like a right hand... either think back to college chemistry or go read up on enantiomers.