Statistical Volume Elements (SVEs) are employed to evaluate homogenized mesoscopic ductile failure response of a carbon nanofiber reinforced composite under uniaxial tensile and compressive loadings. In the mesoscale analysis, after virtual reconstruction of the material microstructure, 2D finite element models are generated for each SVE using a non-iterative meshing algorithm named CISAMR, which fully automates the modeling process. The ductile damage response of each SVE is then simulated to derive its homogenized stress-strain curve. Corresponding initiation, maximum, and failure turning points, together with local fiber volume fraction and homogenized bulk modulus, are defined as mesoscopic Quantities of Interest (QoIs). While compressive loadings have slightly higher strength and nearly twice higher strains at failure compared to similar tensile cases, both loadings yield similar coefficients of variance for most QoIs. Further, a stochastic bulk damage model is calibrated from mesoscopic responses, which takes bilinear and linear forms versus strain for tensile and compressive loadings, respectively. Finally, cross-correlations are made between different QoIs, showing lower strain-based QoIs and higher strengths correspond to either higher local fiber volume fractions or more fibers being aligned with the loading direction. [ABSTRACT FROM AUTHOR]