Under the emission reduction pressure of carbon trading policies (CTP), green innovation (GI) and pollution transfer (PT) are both viable options for meeting emission reduction targets. However, the current research has not systematically considered whether GI and PT coexist or whether there are differences in long-term and short-term dynamic decision making. It is crucial to investigate the dynamic effect of CTP on GI and PT. Taking China's CTP as the quasi-natural experiment, and based on Chinese provincial panel data from 2006 to 2019, this study evaluated decomposed the dynamic effects of CTP on GI and PT using a dynamic spatial difference-in-differences (DSDID) model. The results indicate that, (1) after the CTP promulgation, regional GI increased significantly, accompanied by a more obvious improvement in GI level in pilot areas than in non-pilot areas. The PT in the adjacent areas grew faster than PT in the pilot areas. (2) The CTP had significant long-term direct incentive and spatial spillover effects on GI, but also led to a short-term PT under the “pollution haven effect”. After a series of robustness tests, the dynamic effects were still significant. (3) The “competition for innovation (IC)” significantly enhanced the CTP incentive effect on GI under a siphoning effect, and the “competition for economic (EC)” intensified the PT effect caused by CTP because of collective irrational behavior. (4) In the strong GI capacity areas, the incentive effect of CTP on GI was higher than that in weak GI capacity areas, and the effect on PT was more significant. The mixed quota form driving effect on GI was greater than the free quota form, the free quota form had no significant PT effect on neighboring areas, while the mixed quota form led to a greater PT effect. Based on these findings, further put forward to improve the national carbon trading mechanism and market standards; construct a long-term GI incentive mechanism; account for the differences in local policies and regional joint actions on emissions reductions; construct a local government assessment and supervision mechanisms, which provides policy basis for promoting the “dual carbon” goal.