Translation:My mom threw away my game!
(Notice: the following comment may have influence of my own dialect, so take caution.)
Well, this sentence is a bit weird for me. 丢 and 扔 both means "throw", but they are still a bit different.
丢 is like dumping your waste into the dustbin, however, you have to add a preposition after the verb, like 丢进 (dump into) or 丢到 (throw...to...), otherwise it would mean "to be lost/lose sth."
我的手套丢了。 My gloves are lost.
我丢了我的手套。 I lost my gloves.
扔 is like throwing something really hard (out of your window!). And I think that is probably what the author means. If you think "away" is not translated, you can use “扔掉” instead of "扔".
Same here, 丢掉 is for throwing something away (disposing of it) and to add 弄 for 弄丢了.
The Chinese version sounds as though the mom misplaced/lost (丢失) the game.