The paper is related to the material behaviour of additively manufactured samples obtained by the direct metal laser sintering (DMLS) method from the AlSi10Mg powder. The specimens are subjected to a quasi-static and dynamic compressive loading in a wide range of strain rates and temperatures to investigate the influence of the manufacturing process conditions on the material mechanical properties. For completeness, an analysis of their deformed microstructure is also performed. The obtained results prove the complexity of the material behaviour; therefore, a phenomenological model based on the modified Johnson–Cook approach is proposed. The developed model describes the material behaviour with much better accuracy than the classical constitutive function. The resulted experimental testing and its modelling present the potential of the discussed material and the manufacturing technology.