When you receive an Exotic Animal that you already have in your collection, you will be given an option to keep it on your farm or to sell it. Tap the Sell button if you want to sell the Exotic Animal for an Elixir.

You can also sell an Exotic Animal by tapping the Animal Collection button on your farm.

Then tap the Exotic Animals button.

Select the Exotic Animal by tapping on it, then tap the Sell button.

You will then receive a popup to confirm that you are selling the Exotic Animal for the item shown on its right.

Note: The last Exotic Animal of a Category cannot be sold.