In order to analyze and control surface crack during tube spinning of titanium alloy, six ductile fracture criteria (DFCs) were incorporated into the finite element software (ABAQUS) to simulate the damage evolution in the tube spinning process under various thinning rates. For improving the prediction accuracy of damage evolution during tube spinning, the valid damage strain was proposed to eliminate or diminish the strain fluctuation caused by the ALE adaptive meshing technique. Through analyzing the influence of the equivalent plastic strain, stress state and the principal stresses on the damage accumulation, the mechanisms of surface cracks were revealed. The results show that only the McClintock model predicted that the crack in tube spinning of Ti–15–3 alloy could be eliminated under moderate thinning rates, while lower or higher thinning rates may induce cracking on the tube surface, which was consistent with the experimental results. For the outer layer, as the thinning rate increased, the increasing equivalent plastic strain and tensile principal stresses contributed to the damage accumulation for all the DFCs studied in present research. For the inner layer under moderate thinning rates, the compressive axial and tangential stresses slowed down the damage accumulation, leading to the occurrence of the safe zone of thinning rate (∼20–30%) without surface crack during tube spinning of Ti–15–3 alloy.