The transient vibro-impacts induced by clearance between the connected rotors in driveline system easily causes serious transient noise and vibration, especially between the gear teeth with backlash. To analyze the transient vibro-impacts of the driveline system excited by a step-down engine torque, a new piecewise nonlinear clearance element with time-varying stiffness and oil squeeze damping is proposed, and an 8 degree-of-freedom lumped parameters model with the new piecewise nonlinear clearance elements is established. The transient vibro-impact phenomena of the vehicle driveline during fast disengagement of the clutch are numerically simulated. Colormaps of angular acceleration and vibro-impact force shows the difference of frequency components from transient impact to stable tooth-meshing. The phase plane reveals the phenomenon of multiple impacts and rebounds in each transient impact, and shows the relationship between the relative contact displacement and velocity. The frequency responses of the angular velocity, angular acceleration and vibro-impact forces with time-varying stiffness and linear stiffness are compared respectively. Compared with the widely used clearance element with piecewise linear stiffness, the new nonlinear clearance element with the piecewise nonlinear time-varying stiffness can better reveal the transient vibro-impact responses between the driving and driven gears. Lastly, the transient vibro-impact results of driveline system are verified by the vehicle experiments.