We employed the coarse-grained molecular dynamics simulation method to systematically study the uniaxial supercompression and recovery behavior of multi porous graphene foam, in which a mesoscopic three-dimensional network with hole-graphene flakes was proposed. The network model not only considers the physical cross-links and interlayer van der Waals interactions, but also introduces a hole in the flake to approach the imperfection of pristine graphene and the hierarchical porous configuration of real foam material. We first recreated a typical two-stage supercompression stress strain relationship and the corresponding time-dependent recovery as well as a U-type nominal Poisson ratio. Then the recovery unloading at different strains and multicycle compression-uncompression were both conducted; the initial elastic moduli in the multicycles were found to be the same, and a multilevel residual strain was disclosed. Importantly, the residual strain is not exactly the plastic one, part of which can resurrect in the subsequent loading-unloading-holding. The mesoscopic mechanism of viscoelastic and residual deformation for the recovery can be attributed to the van der Waals repulsion and mechanical interlocking among the hole-flakes; interestingly, the local tensile stress was observed in the virial stress distribution. Particularly, an abnormal turning point in the length-time curve for the mean bead-bond length was captured during the supercompression. After the point, the length abnormally increases for different size ratios of the hole to the flake, which is in line with the mesostructure evolution. The finding may provide a mesoscopic criterion for the supercompression of graphene foam related materials.