We investigate with large-scale molecular dynamics simulations shock-induced surface jetting from grooved Cu as regards microstructure effects, including jetting mass/velocity ratios, directionality, jetting phase diagram, secondary jetting, and underlying mechanisms. The grooves are of wedged, cylindrical, and rectangular shapes. Other microstructure features explored are half angles, crystal structure asymmetry as represented by grain boundaries, geometrical asymmetry, and deformation heterogeneity. The common fundamental mechanism is that jetting is driven by stress gradients due to transverse mass collision. For symmetrical wedged grooves, the velocity ratio (maximum jet head velocity/free surface velocity of flat surface) increases linearly with decreasing half angle, with a slope similar for different materials and at nano- to macroscales, as indicated by our simulations and previous experiments. However, the jetting factor or mass ratio reaches the maximum at certain intermediate half angle. An impact strength vs. half angle phase diagram is established for a typical case of wedged grooves, useful for predicting the critical parameters for jetting (e.g., the critical impact velocity for a given half angle, as well as deducing yield strength). Small asymmetries, including crystal structure and geometrical asymmetries as well as deformation inhomogeneities, may induce considerable deviation of the jetting direction. Wedged, cylindrical, and rectangular grooves form a geometrical hierarchy. Primary jetting can be well described with wedged grooves, and secondary jetting is a result of collision of primary jets. Rectangular grooves may yield pronounced, velocity-enhanced, secondary jetting.