Why is it more dangerous to cut an artery than an ordinary blood vessel?

High Pressure. 1st, i presume the question refers to arteries versus veins, since arteries are "ordinary blood vessels" too. The answer is arteries are in a high pressure system, whereas veins have low pressure . This means that arterial bleeding can be much more significant, and potentially serious, even lethal, rather than venous bleeding, which although may appear impressive, is rarely life-threatening.
Cut an artery. Cut in any artery is dangerous and can be serious.If it happens put ptessure at the site of the artery and keep the pressure and go to the er.