Superelastic porous foam materials can change from soft to hard when subjected to external impacts. At the same time, they can disperse and absorb energy and delay the impact time, possessing extremely strong impact protection ability. To study the energy absorption characteristics of superelastic foam materials and the strengthening mechanism under high strain rates, compression experiments under different strain rates were carried out using an INSTRON 5966 small universal material testing machine and a Φ16 mm split Hopkinson pressure bar (SHPB) experimental system. The energy absorption efficiency, strain rate sensitivity index, and fracture morphology were analyzed. The results show that under quasi-static compression, the stress–strain response of superelastic foam has two-stage characteristics of a slow stress growth region and a rapid stress growth region, and it has an obvious strain rate strengthening effect. Under quasi-static loading, the material has a relatively high energy absorption efficiency, and the strain rate has little influence on the maximum energy absorption efficiency of the material. Under dynamic loading, the superelastic foam material exhibits strain hardening at high strain rates. As the strain rate increases, its yield strength increases from 7 to 9.9 MPa. The fracture strength increases from 9.97 to 15.65 MPa. Under tensile loading, due to the presence of voids inside the material, the material directly fractures at the end of the elastic stage without a plastic deformation stage.