Many studies have been conducted in the last decades on cellular polypropylene (Cell-PP) films. Most of them focus on the optimisation of the material for sensor applications. Processed under Gas Diffusion Expansion (GDE), Cell-PP films show high piezoelectric activity and low stiffness/density, properties that make them ideal for sensors. GDE increases the height and decreases the length over height ratio (aspect ratio) of individual voids within the material. This change in void morphology, and eventually stiffness, results in a nonlinear piezoelectric response of these materials. In this study, a Cell-PP sample was tested under static, quasi-static and low-frequency compressive stress. The main aim is to evaluate its mechanical and piezoelectric properties in the nonlinear region of its response over strain. The load–deflection curves as well as the piezoelectric responses were obtained for stresses up to 270 kPa (engineering strain close to 0.26). It is shown that both the magnitude of the initial load and the strain rate have a critical effect on the creep/stress relaxation of the film and eventually on its piezoelectric response. Finally, it is shown that under dynamic conditions, and for the same engineering strain region, it is more relevant to present the piezoelectric response, in terms of strain rather than stress.