That picture is actually incorrect. When you slash your peripheral blood vessels, the compensatory reaction of your body will not result in a quick death.
By doing what is shown in that picture, you would actually struggle to die. Here is why, when you cut your artery or vein the compensatory measures designed in your body to mitigate fluid loss will become active.
They will cause Vaso constriction, the vain constriction will reduce blood flow from the effected periphery, furthermore as a core design the brain will start to divert the flow of blood to the vitals " Lungs, Heat, Brain" ( You will enter compensatory shock) compensatory shock is when you body is compensating for the loss of fluid by diverting the blood to where it is needed most.
Uncontrolled you will keep bleeding for a very long time before you enter "decompensatory shock" that is when you have vaso dilation, because there is not enough fluid to keep the vessels full you will start to see vessels collapse and have what we call "Hypo-Volemic" : Low Volume Shock.
After you enter hypo-volemic shock your body will no longer be able to compensate for the loss of fluid and the fluid your system will not be sufficient to maintain circulation.
At which point you will suffer organ failure and eventually die of " Exsanguination " AKA: bleeding out. This process is very painful and can take hours.
So... Anyone thinking of slitting their wrists, do yourself a favour and DONT!