What did Mimir do with Odin's eye?
Odin is known to be one-eyed because of a trade between Mimir and Odin. When Odin asked Mimir for some water in the well, Mimir declined him of giving any water unless Odin gave him an eye. Surprisingly, Odin took one of his eyes out and gave it to Mimir for water. The trade was made and Odin was very happy for the water.
But what did Mimir do with Odin's eye? The source tells nothing about the use for Odin's eye or what happens to it.
Odin's eye remains at the bottom of Mimir's Well:
I know where Othin's eye is hidden,
Deep in the wide-famed well of Mimir;
Mead from the pledge of Othin each mom
Does Mimir drink: would you know yet more?
The point of the tale is to convey the message that no sacrifice is too great for wisdom. What happens to Odin's eye after it has been thrown into Mimir's Well is not particularly significant.