Low-value recyclable waste accounts for a large portion of urban waste output in many modern cities. The improper management and disposal of LVRW result in environmental pollution and a waste of resources. Given the characteristics of a high recovery cost and low recovery income of low-value recyclables, it is difficult to obtain a satisfactory waste disposal effect by completely relying on the market mechanism. It is thus necessary for the government to implement effective subsidies for multiple subjects in the urban waste recycling system (UWRS). This study examines the independent roles of four subsidy policies—subsidy to the third-party waste disposal institutions, subsidy to a state-owned waste disposal institution, R&D subsidy for green technology, and subsidy for government publicity—and develops a system dynamics model to verify the performance of the UWRS under different combinations of subsidy-based policies under multiple scenarios. Data on urban waste disposal for Guangzhou from 2019 and 2020 were used to validate and simulate the model. A sensitivity analysis of the main exogenous variables was carried out, and the conclusions are as follows: (1) On the premise of a fixed subsidy capital pool, a mixed subsidy policy produced the best impact on the UWRS. (2) The total subsidy needed to reach a certain threshold; otherwise, the mixed subsidy policy did not improve the UWRS. The total subsidy produced diminishing returns once it had exceeded the threshold. (3) Appropriately reducing subsidies for the third-party waste disposal institutions within a reasonable range does not affect the performance of the UWRS. (4) The effect of government publicity has short-term advantages, while the long-term potential of green technology is greater. Multi-agent coordination and the guidance of the market mechanism are important priorities in the design of subsidy-based policies. In addition, the trade-off between subjects needs attention, and a plan for mixed subsidy policies needs to be designed and implemented according to the response periods of different policies. The research here provides theoretical support for the government for designing subsidy-based policies.