Additive manufacturing (AM) enables the design and fabrication of foams with intricate cell architectures for enhanced mechanical performances in blast and impact mitigation applications. Although the crushing response of AM foams has been studied recently, there is limited research on their failure behaviours under dynamic loading. This work investigates the response of AM Voronoi foams under compressive loadings through a combined experimental and numerical effort, with the emphasis on the failure behaviour and its modelling. Voronoi foams with uniform and graded density distributions were fabricated via the Fused Deposition Modeling technique. Quasi-static (0.001 s−1) and low-speed impact (50 s−1) tests were carried out to quantify the mechanical response and to characterise the deformation and failure behaviours. Computational models of the Voronoi foams were built in ABAQUS and validated with the experiment to provide insights into the dynamic fracture behaviours. Results showed that although failure plays a minor role in the quasi-static loading case, dynamic compressive loading can yield complex fracture behaviours involving cell-wall buckling, cell-wall rupturing, large-scale shattering and shear band localisation, resulting in significant stress softening and strong stress fluctuations during the post-yield response. Consequently, the load-bearing and energy absorbing capacities materially deteriorated when transiting from quasi-static to dynamic loading conditions. The results reported in this work provide valuable guidance on the design of AM foams under dynamic loadings.