The surgeon is called in after Billy strikes Claggart. He can immediately see that Claggart is dead, but he checks anyway. When the surgeon hears the Captain's plans for dealing with Budd, he thinks that they are unnatural. He wonders if perhaps Vere has become unhinged, but he has no way of knowing and he can't simply step forward and suggest that he is insane. As the narrator says, "To argue his order to him would be insolence. To resist him would be mutiny" (20.2). In short, there is no way for the surgeon to question the Captain's behavior no matter how much he disagrees with it.
The surgeon makes another appearance after Billy's death. The Purser, the ship's accountant, thinks the fact that Billy did not twitch after he was hung was a sign of Billy's willpower. The surgeon, in his dry scientific way, explains that it was probably just a lack of muscle twitch. He says, "It was phenomenal, Mr. Purser, in the sense that it was an appearance the cause of which is not immediately to be assigned" (26.7). In this mini-debate between faith and science, the surgeon acts as the voice of science.