Rooted in the Titan War story Zeus cut up Kronos with his own scythe when he took over the throne of the heavens. From this we get the image of the old king (Kronos = Old Year) with his scythe getting displaced by the baby (Zeus = New Year Baby).
Cronus is often represented as an old man leaning on a scythe, with an hour-glass in his hand. The hour-glass symbolizes the fast-fleeting moments as they succeed each other unceasingly; the scythe is emblematical of time, which mows down all before it.