Um, you know actually cutting your wrist vertically will kill you right? Since you are in essence slicing directly down your vein. As opposed to horizontally, where you just slice it open and have a higher chance of survival if help arrives, etc. But if vertically, your time is shortened immensely. So, they would have to use magic to cast the spell, then even more magic to heal themselves so they won’t bleed out.
As the saying goes, its down the road, not across the street. However in most movies they cut across, not sure why. Maybe they don’t want to give those contemplating suicide the actual way?