The present disclosure provides a belt transmission device and a grinding apparatus. The device comprises: a grinding stand; rotation wheels mounted on the grinding stand, including a driver wheel and driven wheels; a grinding belt supported by rotation wheels; a first sensor fixedly provided on the grinding stand and configured to detect a rotation speed of any one of the driven wheels; and a controller configured to control a rotation speed of the driver wheel and connected with a driving motor of the driver wheel, wherein the controller is further connected with the first sensor, receives rotation speed signals of the one driven wheel detected by the first sensor, calculates difference between the rotation speeds of the driver wheel and the one driven wheel, and compares the difference with a predetermined difference range in the controller; and when the difference is beyond the predetermined difference range, an alarm is provided.