CdTe photovoltaic modules are the most commercially successful thin-film solar cells. In particular, flexible CdTe modules are a promising development in photovoltaic architecture. Cd2SnO4 (CTO) is a low-cost transparent conductive material with excellent optical and electrical properties. Although laser scribing is commonly used to produce cell interconnects in the manufacturing of thin-film PV modules, the laser scribing process window for CTO-based CdTe cells is narrow, and more research is needed on direct laser scribing of flexible CdTe solar cells. In this study, the picosecond pulsed laser scribing of CdTe solar cells with CTO front electrodes and flexible glass substrates was investigated using lasers with the wavelengths of 355 and 532 nm. The flexible cells were suctioned onto a working platform, and a direct ablation method was adopted. The damage and removal thresholds of the CTO, CdTe, and Ni layers were studied and the effects of the spot spacing, multilayer conditions, and laser polarization state were investigated. A method for determining the scribing parameters was proposed. Very smooth scribing grooves were obtained using the optimized laser scribing process. The series and shunt resistances of the cells after laser scribing showed no significant differences compared to those of the control cells.