In literature, the concept of material gradation is shown to inhibit surface crack initiation in glass/ceramic composites subjected to Hertzian indentation. However, surface cracks could yet initiate due to relatively higher loadings or in the presence of surface flaws/defects. Hence, characterization of graded composites concerning the resistance against Hertzian crack initiation and propagation manifests itself as a prominent matter. In this study, axisymmetric Hertzian cracks evolving in graded glass/ceramic composites propelled by a rigid cylindrical punch are investigated employing a novel recursive method, called the stacked-node propagation procedure. Crack trajectories and their propagation susceptibilities are predicted via the minimum strain energy density (MSED) criterion regarding the crack growth resistance (R-curve) of ceramics. The stress trajectory approach is also considered for a homogeneous glass to reveal the reliance and effectiveness of the MSED criterion in the present crack problems. The Mori–Tanaka relations are adopted to model the elastic modulus and Poisson's ratio variations through the composites, which are implemented on the simulations via the homogeneous finite element approach. Hertzian crack problem of a practically producible graded composite comprised of oxynitride glass and a fine-grained silicon nitride ceramics (Si3N4) is treated as a case study. The degree of material gradation is assessed for the mitigation of surface crack initiation and propagation risks.