A glass edge finishing system, a belt assembly and a method are described herein for finishing an edge of a glass sheet. The glass edge finishing system comprises: (a) a base; and (b) one or more belt assemblies located on the base, where each belt assembly includes: (i) a support frame; (ii) a motor; (iii) a pair of pulleys rotatably mounted on the support frame and driven by the motor; (iv) a belt engaged to and driven by the pair of pulleys, where the belt contacts and finishes the edge of the glass sheet; (v) a belt cleaning device that removes glass debris from the belt as the belt moves past the belt cleaning device; and (vi) a cleaning containment enclosure within which there is located the belt cleaning device, where the cleaning containment enclosure contains the glass debris removed from the belt by the belt cleaning device.