Blood doesn’t circulate through your body one body part at a time. Don’t imagine a big ring road that loops first through your arm, then through your torso, then through your leg, etc. Instead, imagine a big tree-like network with big highways coming from the trunk, which split into smaller roads, which split into streets and finally driveways. And then imagine that each road has traffic going in both directions, separated by a median divider. One direction is an artery, the other is a vein. That’s what your vascular system is like. Blood is being pumped, in parallel, through arteries that carry oxygen-rich blood from the heart to where it is needed, and then back, through veins, that carry the oxygen-depleted blood back to the heart (and then there is a separate loop through the lungs, where arteries carry oxygen-depleted blood away from the heart to the lungs, and veins return the newly oxygenated blood back to the heart to be distributed to the body).
If your leg is cut off, or something similarly severe, it’s like one big branch of the tree being severed. Its a big problem because you can lose a lot of blood that way, but it doesn’t (directly) prevent blood going to places whose branches are still intact (at least, not in the way that you’re imagining – the loss of blood (pressure) can of course lead to a lack of blood going to those places after all).
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