The reconstruction and expansion project of oil reserve base often faces the excavation and blasting of the slope and undercrossing tunnel at the same time. Due to the flammable and explosive liquid storage nearby, the tight construction period, and the high requirements of collaborative construction, once the blasting accident occurs, the consequences are unimaginable. To facilitate safe and timely cooperative blasting construction of the slope and undercrossing tunnel, a vibration monitoring test of the slope and tunnel surrounding rock is conducted. The vibration response characteristics of the rock surrounding the slope and tunnel are analyzed, and a mathematical prediction model for the peak particle velocity (PPV) with consideration of the influence of the relative slope gradient (H/D) is established based on dimension analysis theory, which improves the prediction accuracy of PPV at the slope surface. ANSYS/LS-DYNA is used to establish a 3D finite element model for the slope and tunnel, and the dynamic response of the tunnel surrounding rock under blasting load is verified through field monitoring data. A linear statistical relationship between PPV and effective tensile stress (ETS) of the tunnel surrounding rock is established. The PPV safety criterion of the tunnel surrounding rock under blasting load is proposed to be 10 cm/s according to the first strength theory, and hence, the minimum safety distance from the tunnel working face to the slope surface is calculated to be 36 m. Finally, the excavation timing arrangement of the slope and tunnel is proposed, which has been successfully applied to the expansion project, and the construction period has been effectively shortened by 45 days while ensuring construction safety. The research results have great guiding significance to similar cooperative blasting excavation engineering for high slope and adjacent tunnel with safety and efficiency.