Nice theme. Is this missing a mechanic, though? It's not clear what "performing surgery" is, or how you get to stand back up after losing an organ.

Aha, yes, that makes it much clearer.

I really like the fact you're getting points for helping people rather than wounding them - although you say that in most cases it's going to be the "player who fired upon them" who performs the surgery, presumably there's plenty of scope for skulking and watching a medic shoot someone, and then shooting that medic yourself so that they're both down, and you can grab a card from each.