The study presents an analysis of the cracking process of explosive welded layered material AA2519–AA1050–Ti6Al4V (Al–Ti laminate) at ambient (293 K) and reduced (223 and 77 K) temperatures. Fracture toughness tests were conducted for specimens made of base materials and Al–Ti laminate. As a result of loading, delamination cracking occurred in the bonding layer of specimens made from Al–Ti laminate. To define the crack mechanisms that occur at the tested temperatures, a fracture analysis was made using a scanning electron microscope. Moreover, acoustic emission (AE) signals were recorded while loading. AE signals were segregated to link their groups with respective cracking process mechanisms. Numerical models of the tested specimens were developed, taking into account the complexity of the laminate structure and the ambiguity of the cracking process. A load simulation using the finite element method FEM allowed calculating stress distributions in the local area in the crack tip of the Al–Ti laminate specimens, which enabled the explanation of significant material cracking process development aspects. Results analysis showed an influence of interlayer delamination crack growth on the process of the Al–Ti laminate specimen cracking and the level of KQ characteristics at different temperatures.