Core testing is a valuable experimental method for characterizing materials from existing structures, particularly when extracting large specimens or full assemblies is impractical. Depending on the testing setup, core samples can provide insights into material behaviour under various loading conditions, aiding in the evaluation of structural integrity, deterioration, and performance. This method can support forensic engineering efforts, helping to diagnose deficiencies and inform targeted preservation strategies. However, extracting core samples from existing structures presents several challenges, particularly the potential inclusion of defects such as cracking, debonding, and material loss. To examine the impact of these morphological irregularities on material characterization results, a computational framework based on the discrete element method (DEM) is employed. This framework discretizes the internal geometry of quasi-brittle materials into pseudo-three-dimensional triangular blocks, allowing for detailed tracking of fracture initiation, propagation, and crack coalescence. The modelling approach is first validated against experimental brick core testing to ensure its ability to capture specimen behaviour, including load-bearing capacity and failure mechanisms. Following validation, the framework is extended to investigate the impact of internal defects on the mechanical response of masonry cores. These analyses provide valuable insights into the potential influence of pre-existing defects on material characterization from extracted core samples, enhancing the understanding of heritage materials and informing improved conservation strategies.