Use 'chuck away' to describe getting rid of things, but remember some items need special disposal methods. Don't just chuck away batteries; they need to be recycled properly.
Pro Tip 2/3
Casual Conversation
Most appropriate in casual settings; may sound too informal in professional or academic situations. I'm going to chuck away these old magazines unless you want them.
Pro Tip 3/3
Physical Action
Implies a physical action of throwing something into the bin or garbage. Just chuck away those torn papers in the recycling bin.