Abstract Spinnability, the maximum thickness reduction ratio a material can undergo without fracture, has important effects on product quality and production efficiency in tube spinning. However, predicting the rupture limit and spinnability poses challenges due to the complexity of tube spinning process. This study aims to select appropriate ductile fracture criteria (DFCs) in terms of the damage limits, which were obtained by mechanical tests, to accurately predict the forming limit and damage evolution in the tube spinnability test. The periodic stress triaxiality and periodic Lode parameter were firstly introduced by considering the periodical changes of the stress and strain components in the spinning process. Based on the evolution of the two parameters, the out layer of TA2 titanium tube exhibited a higher damage potential, which was consistent with the experiment results. Nine ductile fracture criteria were incorporated into the finite element software (ABAQUS) to simulate the damage evolution in tube spinnability tests. The results show that, except for the Freudenthal, R–T and Ayada models, all of the other ductile fracture criteria are suitable for predicting the damage distribution on TA2 titanium tubes in spinnability tests. The variation of stress triaxiality under different cut-off values in tensile test were much closer to that in spinnability test relative to upsetting test throughout the entire forming process, which led to higher prediction accuracy of the spinnability by the tensile test. For all of the DFCs considered, the C–L criterion provides the most accurate predictions on the spinnability of TA2 titanium tubes.