The experimental characterization of mortar mechanical properties in existing masonry constructions is considerably complex. Whereas bricks parameters can be assessed with a sufficient precision, the mortar properties are very difficult to obtain and the results are highly dispersed. For instance, the in-situ techniques based on the measurement of the amount of energy required to drill a small cavity provide very scattered values that should be handled cautiously. Also, the characterization of existing mortar joints by means of surface testing may be difficult, since the surface decay or even the presence of new restoration mortar may spoil the results. On the other hand, tests on small mortar cubes or double punch tests usually lead to inaccurate estimates of mechanical characteristics, since the confining effect exercised by bricks on the mortar layer is completely disregarded. Another difficulty is the extraction of undisturbed specimens from the joints of existing brickwork. Such problems can be overcome by laboratory destructive testing on small specimens including both bricks and mortar. This activity is suitable for existing historic buildings, since it does not inflict severe damage on the structural element. This work presents the results of a comprehensive experimental program on cores including a central mortar layer along a symmetry plane. Such specimens were easily extracted by different panels of an existing historical building using a common core drill. The cores were subjected to splitting test with a particular set-up, providing 30°, 45° or 60° inclinations of the mortar layer with respect to the loading plane. This test induces a mixed compression–shear stress state in the central mortar layer. The experimental results have been interpreted using different failure criteria in order to assess the mechanical properties of mortar.