The sign for throw away is very simple. Your dominant hand picks up an invisible piece of paper from the palm of your non-dominant hand (which should be facing upward), then you proceed to cast it away a bit to the side.
A more popular, currently used ASL sign for throw away looks a bit like grab, with an added gesture of throwing away. You take your open number 5 hand, twirl it once in the air, then close it into a fist as if you are grabbing something, then you open your '5' hand again and cast it to the side.
We use the sign for throw away when we are teaching our babies about hygiene and trying to encourage them to be helpful by taking small pieces of garbage to the bin.
Teach your toddler the throw away sign when you see they are ready to learn about keeping tidy at home and when outside in public spaces.