Santiago would be defeated if he gave up. He refused to give up, no matter what it did to him to keep up the struggle. The basic idea is that Santiago is tough
Santiago has gone a long time (87 days, I believe) without catching a fish. Despite that, he keeps going out and fishing. Santiago has caught himself a fish which is bigger than his boat and which he can't reasonably expect to bring back without trouble. Despite that, he does his best to bring the fish home. Santiago's body is not cooperating during this exhausting endeavor. Despite that, he does what he must to catch bring in the marlin. Santiago's great fish is attacked by sharks. Despite that, he defends his "brother" the best he can. At the end of his ordeal, he has a broken body and a broken fish, which by anyone's definition spells defeat, yet Santiago is not defeated. We know he will go out again tomorrow and fish.
Santiago's struggle against the marlin is one of classic and epic proportions. Although he is not successful is bringing the fish back to shore, he proves that it can be done. He may have been unsuccessful--his catch may have been destroyed--but he was not defeated and in fact returns to the seas and a more knowledgeable, more experienced fisherman.