Forming limit diagram (FLD) is a crucial tool for assessing the formability of sheet metals under various forming conditions. However, conducting FLD experiments can be challenging and time-consuming requiring numerical determination of FLDs. Marciniak-Kuczyński (M-K) theory is one of the most well-known instability criteria for calculating forming limits, and the rapid development of crystal plasticity models provides a feasible framework for better understanding the relation between flow localization and material microstructure. Therefore, integrating the M-K theory with advanced crystal plasticity models offers a potential approach to precisely predict forming limits and explore the complex interaction between material behavior and microstructural characteristics. In this study, a crystal plasticity finite element (CPFE) model considering damage evolution was developed based on the microstructure and crystal orientation of a TA32 titanium alloy sheet. The material parameters for the proposed model were calibrated through uniaxial tensile tests and microstructure characterization. The internal correlation between damage evolution and the dislocation slip mechanism under different strain paths was analyzed at the grain scale. Additionally, the FLD of the TA32 sheet at 750 ^oC was predicted by coupling the CPFE model with the M-K theory. The results show that the proposed CPFE model accurately predicts the macroscopic mechanical response, microscopic inhomogeneous deformation, and damage evolution behavior of the TA32 sheet under different strain rates at 750 ^oC. The difference in the deformation behavior and damage propagation was mainly attributed to the anisotropic activation of various slip systems. The basal and prismatic slip systems of the basal bimodal texture in the original sheet were difficult to be activated under different strain paths, making it easier to induce damage than the transverse texture. The FLD predicted by the CPFE-M-K coupling model agrees well with the Nakazima test results, accurately capturing the decrease in the limit of major strain near the equibiaxial tensile region. This decrease is closely related to the anisotropy of the mechanical properties of the material. Furthermore, the change in the initial inclination angle of the groove in the CPFE-M-K coupling model considerably affects the prediction accuracy of the forming limits of the TA32 sheet. The critical initial inclination angles within the strain increment ratio ranges of -0.5-0.5 and 0.6-1.0 are 0° and 90°, respectively.