Mechanical avalanches during compression of martensitic porous Ti-Ni have been characterized by high-frequency acoustic emission (AE). Two sequences of AE signals were found in the same sample. The first sequence is mainly generated by detwinning at the early stages of compression while fracture dominates the later stages. Fracture also determines the catastrophic failure (big crash). For high-porosity samples, the AE energies of both sequences display power-law distributions with exponents ɛ≃2 (twinning) and 1.7 (fracture). The two power laws confirm that twinning and fracture both lead to avalanche criticality during compression. As twinning precedes fracture, the observation of twinning allows us to predict incipient fracture of the porous shape memory material as an early warning sign (i.e., in bone implants) before the fracture collapse actually happens.