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Due to the complex diagenesis process, basalt usually contains defects in the form of amygdales formed by diagenetic bubbles, which affect its mechanical properties. In this study, a synthetic rock mass method (SRM) based on the combination of discrete fracture network (DFN) and finite-discrete element method (FDEM) is applied to characterizing the amygdaloidal basalt, and to systematically exploring the effects of the development characteristics of amygdales and sample sizes on the mechanical properties of basalt. The results show that with increasing amygdale content, the elastic modulus (E) increases linearly, while the uniaxial compressive strength (UCS) shows an exponential or logarithmic decay. When the orientation of amygdales is between 0° and 90°, basalt shows a relatively pronounced strength and stiffness anisotropy. Based on the analysis of the geometric and mechanical properties, the representative element volume (REV) size of amygdaloidal basalt blocks is determined to be 200 mm, and the mechanical properties obtained on this scale can be regarded as the properties of the equivalent continuum. The results of this research are of value to the understanding of the mechanical properties of amygdaloidal basalt, so as to guide the formulation of engineering design schemes more accurately.