Crack propagation under mixed-mode (I + II) conditions has been investigated in a semicircular disc where various levels of mixed-mode can be achieved by means of different geometry configurations. The research has been performed on a novel cementitious material, alkali-activated concrete. Its main advantage is that it is environment-friendly. On the other hand, its fracture mechanical properties, as of yet, have not been described sufficiently. Therefore, a fracture analysis has been performed. The crack deflection under threepoint bending conditions has been investigated numerically as well as experimentally. The numerical approach is based on a combination of the common finite element analysis and a multi-parameter form of the maximum tangential stress criterion. This generalized method is suitable especially for materials with specific (elasto-plastic, quasi-brittle etc.) fracture behaviour. The over-deterministic method together with the Williams expansion is applied to approximate selected stress tensor components around the crack tip. In this work, the influence of the eccentric crack is also discussed. In the conclusions, several recommendations about using single-parameter/multi-parameter fracture mechanics are stated.