Drop impact causes severe surface erosion, dictating many important natural, environmental and engineering processes and calling for substantial prevention and preservation efforts. Nevertheless, despite extensive studies on the kinematic features of impacting drops over the last two decades, the dynamic process that leads to the drop-impact erosion is still far from clear. Here, we develop a method of high-speed stress microscopy, which measures the key dynamic properties of drop impact responsible for erosion, i.e., the shear stress and pressure distributions of impacting drops, with unprecedented spatiotemporal resolutions. Our experiments reveal the fast propagation of self-similar noncentral stress maxima underneath impacting drops and quantify the shear force on impacted substrates. Moreover, we examine the deformation of elastic substrates under impact and uncover impact-induced surface shock waves. Our study opens the door for quantitative measurements of the impact stress of liquid drops and sheds light on the origin of low-speed drop-impact erosion.