The increasing threat of global climate change is primarily caused by rising carbon emissions, with cities acting as significant contributors. This study bridges two vital gaps in urban carbon neutrality research: unraveling the causal dynamics of carbon emissions within urban networks and forecasting emission trends. This study proposes a reinforcement learning-based causal discovery algorithm, progressively deciphering the complex causal relationships in global urban emissions, and facilitating the creation of directed acyclic causal graphs. Furthermore, a hyperbolic graph neural network-based forecasting algorithm is introduced, through integrated fusion curvature to improve the information transfer between cities, for predicting global urban emission trends. A comparative analysis positions these innovative algorithms against leading methods, using emission data from thousands of cities for predictions one, five, and ten steps ahead. The experiment employs prediction error metrics, Taylor statistics, the Diebold-Mariano test, and the ablation analysis for validation. Results reveal proposed causal discovery algorithm effectively identifies the causality of carbon emissions among cities, while the forecasting algorithm leads other competing models across all prediction ranges. Based on the effectiveness of the algorithms, this study decodes the significant nature of the global urban carbon emission network, offering policy insights for collaborative carbon mitigation in cities worldwide.