In the context of the dual carbon goals, achieving low-carbon development is a necessary path for high carbon emitting enterprises to achieve high-quality growth in China. Carbon resilience was introduced as a new concept. It is argued that carbon resilience, as a special dynamic capability for enterprises to cope with the impact of the "dual carbon" goals, can help high carbon emitting enterprises achieve growth. Digital transformation is identified as a vital mechanism through which carbon resilience affects the growth of high carbon emitting enterprises. Based on the dynamic capabilities theory, the nonlinear impact of carbon resilience on the growth performance of high carbon emitting enterprises and its mechanism of action were empirically analyzed. The impact of the heterogeneity of digital transformation stages on high carbon emitting enterprises is further explored. The results show that carbon resilience has a "U-shaped" impact on the growth performance of high carbon emitting enterprises. As the level of carbon resilience increases, its impact on the growth performance of high carbon emitting enterprises first decreases and then increases in a nonlinear manner. The digital transformation strategy plays a mediating role between carbon resilience and the growth performance of high carbon emitting enterprises. Further research finds that for high carbon emitting enterprises in the digital transformation stages of single-point deepening and comprehensive integration and reconstruction, the "U-shaped" relationship is more pronounced. The conclusions deepen the understanding of the relationship between carbon resilience and the growth performance of high carbon emitting enterprises. They provide important references for the growth of high carbon emitting enterprises and offer new ideas for guiding these enterprises to effectively enhance the effectiveness of their digital transformation.