Poop

How to Get Poop
Throw any animal or Nym, or hit them with your tools like your axe. They will be displeased and spit out poop onto the ground.

You don't. There is no way to get rid of poop.
The devs of Raccoon Lagoon have designed the game so that once you get poop, there is no way to throw it away. This is meant to be a little punishment of sorts for players who are mean to their Nyms.

So how else can you deal with poop?
The best ways are to buy a chest from any shop that you can use to store items in, and place your poop inside. You can then either leave the chest, or put it into your inventory, and the poop will no longer be sitting on your island out in the open.