To throw away is to put something in the bin for good. Gone, and not coming back.
It splits round an object, so you throw something away. The figurative sense is about waste, and throwing away a chance, a lead or your money means losing it through carelessness rather than bad luck, which is why the phrase carries reproach. A throwaway remark is one made casually, and throwaway packaging is designed to be discarded, which is now a criticism rather than a selling point.
1phrasethrow awayTo discard something as rubbish.
“Do not throw away the instructions.”
2phrasewasteTo waste an opportunity or advantage.
“They managed to throw away a two-goal lead.”
Also accepted in games: throw out, discard
From throw + away. late 14c.
Etymology from Wiktionary, CC BY-SA