You can die when your wrists are slit, because: If you slit your wrist (especially if you slit it vertically), you are slashing an artery that runs directly to your heart. You will quickly "bleed out" internally from that slashed artery, unless you receive immediate medical attention.
If your hand is blown off or cut off, your hand doesn't contain arteries, it only contains veins. Many times today (if your hand is cut off), the hand can be re-attached to your arm, after the veins and bones are put back together. You're not in as much danger of "bleeding out" from a hand that is cut off as you would be from a slashed artery. In fact, a hand that's cut off doesn't "bleed" as much as you would expect It would - you're only cutting veins..