Abstract: To achieve carbon neutrality by 2060, China has set stricter energy-saving targets, and it is important to evaluate the effects of these targets' policies scientifically. The study finds that the energy-saving targets reduce the scale of carbon emissions, increase the total amount of carbon replacement, and effectively improve cities' carbon neutrality. At the same time, the energy-saving targets promote the carbon neutrality level of the city by strengthening the "top-down" promotion pressure and policy pressure, as well as the "bottom-up" transformation pressure and public opinion pressure. It is worth noting that the pressure of corporate transformation is the backbone of carbon neutrality, while public opinion monitoring with public participation has a limited effect on carbon neutrality. In addition, energy-saving targets have formed a complex and intertwined network of competition and transfer between different cities. Among cities in the same "situation", energy-saving targets will positively promote carbon neutrality in other cities, while among cities with development gaps, the carbon neutrality effect of energy-saving targets shows a significant siphoning effect. Interestingly, energy-saving policy targets in energy-endowed cities favour carbon neutrality enhancement in energy-poor cities. Therefore, it is important to focus on the role of public opinion supervision. The competition in the horizontal dimension needs to establish a benign mechanism, and the transfer in the vertical dimension should be flexibly managed based on the energy output rate.