Why is it that when people slit their wrists they die but when they get their hand cut off they don't die?

People don't always die from cutting their wrists, it's just the fact that there is a main artery there, so if they cut it they will be pumping out excessive amounts of blood. However, someone that cuts their hand off is usually around other people and so they will call an ambulance who will usually provide aid to the wounded and they will survive.

When you guillitine-sever blood vessels, a reflex constricts the vessel and usually shuts it down. Even arteries will typically shut down without help if the cut is clean and perpendicular to the vessel.

Also, the majority of people who attempt suicide by cutting their wrists actually recover.