Yoshi's Egg is a special item that only appears in Event 13: Yoshi's Egg. This Yoshi's Egg should not be confused with Yoshi's Up B move.
Yoshi's Egg can be picked up and tossed around. That is not the point of the item though. The point of the item is to prevent it from being destoryed. The egg will break after it drops or is thrown constantly.