The mechanical behavior of core/shell nanoparticles (CS-NPs) with a cubic diamond crystalline core and an amorphous carbon shell was investigated through molecular dynamics simulations using indentation tests. Different CS-NPs were considered, all with a 10 nm core diameter but varying shell thicknesses ranging from 0.0 to 6.5 nm. Indentation revealed a similar elastic response followed by plastic deformation. Increasing shell thickness resulted in a softening effect, with reductions in both maximum and flow contact stress. The MultiSOM machine learning algorithm was used to detect the evolution of several phases in the initially cubic-diamond NP core. Analysis of the plastic deformation mechanisms revealed dislocation nucleation and amorphization within the core, pushing atoms at the core-shell interface and inducing shear transformation zones, which did not evolve into shear bands crossing the shell as observed in other amorphous materials. The degree of strain localization in the amorphous shell increased with shell thickness. Therefore, as shell thickness increased, amorphous shell deformation accommodated a larger fraction of the strain, decreasing dislocation nucleation but allowing more extensive amorphization in the core, with no dislocations at large strain for the thickest shell studied. These results highlight the key role of amorphous shell thickness in determining the elastic and plastic deformation behavior of CS-NPs. Shell thickness is a critical factor in both the onset of plasticity and the nature of deformation mechanisms.