Odysseus at length succeeded in making Polyphemus drunk, blinded him by plunging a burning stake into his eye while he lay asleep, and, with six of his friends (the others having been devoured by Polyphemus), made his escape by clinging to the bellies of the sheep let out to pasture.

Why did Odysseus blind the Cyclops?

The liquor is very good, so the Cyclops will want more of it. Since Odysseus and his men are trapped inside the cave, they cannot kill the Cyclops, so they decide to blind him instead.

Why does Odysseus blind Polyphemus rather than kill him?

Polyphemus says that he'll eat Odysseus last. Why does Odysseus blind Polyphemus rather than kill him? ... To ensure that the man is really Odysseus because he is the only one who knows everything about their bed.