In one aspect, a system for controlling the operation of rotating ground-engaging components of an agricultural implement may include a rotating ground-engaging component configured to rotate relative to soil within a field as the agricultural implement is moved across the field. The system may also include a rotational speed sensor configured to capture data indicative of a rotational speed of the ground-engaging component. A controller of the system may be configured to monitor a first-order derivative of the rotational speed of the ground-engaging component based on data received from the rotational speed sensor. Moreover, the controller may be configured to determine when a frequency of the monitored first-order derivative falls outside of a predetermined frequency range. Additionally, the controller may be configured to initiate an adjustment of an operating parameter of the ground-engaging component to return the frequency of the first-order derivative to within the predetermined frequency range.