The deployment of intelligent transportation systems (ITS) in emerging urban areas faces significant challenges due to the scarcity of historical data. Knowledge transfer across cities has shown exciting potential in addressing this issue, yet existing methods typically rely on predefined or static graphs, neglecting dynamic spatio-temporal relationships. Moreover, they handle data distribution discrepancies solely at the domain or node level, neglecting the multi-granularity heterogeneity inherent in urban data distributions. In this paper, we propose a Dynamic Graph-based Cross-city Traffic Prediction Framework (DGCTF), which introduces an adaptive graph structure learner to capture dynamic spatio-temporal relationships and complex interdependencies among cities. Besides, DGCTF addresses data discrepancy issue at multiple granularities. At the domain-level, DGCTF reduces data distribution differences across cities through a cross-domain feature alignment training method with Cross-Domain Feature Alignment Loss (CDFAL). At the node-level, DGCTF enables fine-grained adaptation via a Residual-enhanced GRU with Node-level Parameter-Matching strategy (RGRU-NodePM) by generating node-specific parameters to model node correlations across cities. Experimental results on multiple real-world datasets demonstrate that DGCTF significantly outperforms state-of-the-art methods in both short-term and long-term predictions. Notably, in several cross-city prediction tasks, DGCTF outperforms the second-best methods by up to 5.78% in MAE, 2.39% in RMSE, and 8.65% in MAPE.