I've had this come up a couple times in games. You're narrating back and forth, the shared imagined space is rich, everyone is having a good time with your specific story game. And then someone starts bleeding profusely.
It's tricky, because:
(A) they're getting the book and the character sheets all soaked in blood,
(B) it's difficult to read die results when they're covered in blood,
(C) they could die,
(D) some people in the group might get uncomfortable about that fleshy content,
(E) panic could ensue.
Now, some of you will probably suggest that I should just rely on tried-and-tested social contract tools, like lines ("You can't bleed here") and veils ("You can bleed, but I don't want to see it or hear about it"). But I think this situation is a bit more complicated and nuanced than that. So I think it warrants its own conversation.
But I'm not really sure where this conversation should go. Should we talk about how/why people end up bleeding at our gaming tables? Should we talk about how to staunch the bleeding, given different types of cuts and punctures? Should we talk about how you handle bleeding risks, like people asking to bring machetes to the gaming table? The floor is open. Take this conversation in any direction you care to.