Most people know that our bodies contain large arteries which control the major blood flow in our bodies.
But we actually have other tiny veins in our body near the surface of our skin that gets cut open when we cut our skin.
So when you get a minor cut of your skin that is not too severe then you actually do cut open a vein for blood but it's just a tiny vein.
And usually small cuts like that will heal themselves with a bandage or some flour without the need for stitches.
If the vein is a bigger vein that you cut then you need medical treatment to prevent the blood from flowing out of your body at too fast of a rate which can then lead to death.
We need blood to survive and when you lose too much blood then your heart can't pump the needed blood to our bodies.
Then you die as a result if you don't replenish that blood through a transfusion.
Just like a cars engine would stop running if there was no oil your heart would stop pumping and then you'd die as a result of no blood in your body.
So you do cut a small vein in your body but it's not a big vein that would cause a problem as long as you stop the blood flow.
The smaller blood vessel also has lower blood pressure in it than the larger blood vessels so you don't bleed out as fast.