The traditionally accepted source of Anomalous Cosmic Rays (ACRs) is neutral atoms penetrating the heliosphere from the local interstellar cloud (LIC). The ACR composition should be depleted in easily ionized atoms such as C, Si, and Fe. However, significant fluxes of these ions are observed in ACRs and their source has not been previously identified. We show that there is an outer source of pickup ions, and hence ACRs, caused by sputtered atoms (subsequently ionized and picked up by the solar wind) from small grains generated via collisions of objects in the Edgeworth-Kuiper Belt. The outer source accounts for the abundance and composition of the additional population of ACRs. The discovery that ACRs are generated from material in the Edgeworth-Kuiper Belt provides an exciting new tool for understanding the mass distribution and composition of the Edgeworth-Kuiper Belt, and for probing the plasma-dust interactions in stellar environments.