Soft granular assemblies are encountered in many natural systems and are important motifs in many engineered applications, from powder compaction to pharmaceuticals and biosystems. Understanding the mechanical behaviors of such granular systems is essential for their translational applications. It is understood that the mechanics of these systems is fundamentally rooted in the inter-particle interactions associated with deformable contact mechanics. Yet, full-scale discrete element method (DEM) simulations become important as complex multi-particle interactions can occur in such assemblies. We study the nonlinear mechanics of two-dimensional hyperelastic granular packings using finite element-based DEM under compressive loading. The focus is on developing a statistical mapping between the macroscopic force-displacement relations and the porosity evolution as a function of the particle compressibility. The macroscopic behaviors are correlated with the emergent micromechanical features of pore size and shape distributions and their orientation distributions. These micromechanical features offer insights into potential failure behaviors of such assemblies under tensile loading states.