A structured abrasive article comprises a backing with a topographically structured abrasive layer secured thereto. The topographically structured abrasive layer comprises precisely-shaped abrasive composites. A solid overlayer comprising eroding particles with a Mohs scale hardness of at least 4 and a water-soluble polymer is disposed on at least a portion of the topographically structured abrasive layer. Methods of making and using the structured abrasive articles are also disclosed.