Santiago knows that the hook can kill the fish, and he hopes at first that it will. He tells the fish,
"Eat it well...eat it so that the point of the hook goes into your heart and kills you".
Santiago quickly realizes, though, that in this case, the hook is not going to kill the fish. He thinks that the outcome of this particular situation might be that the fish, caught by the hook, will pull the boat until it becomes exhausted. At that point, he predicts that the fish will "come up easy and let (him) put the harpoon into (him)".
Santiago remembers a time when he killed a fish in just this way. There was a pair of marlin in that particular situation, and Santiago had hooked the female. The stricken fish "made a wild, panic-stricken, despairing fight that soon exhausted her", and when she was spent, Santiago was able to draw her close, gaff her, and club her to death. In a note of extreme pathos, the male fish stayed close through the whole process, jumping high into the air next to the boat when the body of his mate was drawn on board. Santiago remembers the incident as "the saddest thing (he) ever saw".