Spiking neural networks (SNNs) are artificial neural networks based on simulated biological neurons and have attracted much attention in recent artificial intelligence technology studies. The dendrites in biological neurons have efficient information processing ability and computational power; however, the neurons of SNNs rarely match the complex structure of the dendrites. Inspired by the nonlinear structure and highly sparse properties of neuronal dendrites, in this study, we propose an efficient, lightweight SNN method with nonlinear pruning and dendritic integration (NSPDI-SNN). In this method, we introduce nonlinear dendritic integration (NDI) to improve the representation of the spatiotemporal information of neurons. We implement heterogeneous state transition ratios of dendritic spines and construct a new and flexible nonlinear synaptic pruning (NSP) method to achieve the high sparsity of SNN. We conducted systematic experiments on three benchmark datasets (DVS128 Gesture, CIFAR10-DVS, and CIFAR10) and extended the evaluation to two complex tasks (speech recognition and reinforcement learning-based maze navigation task). Across all tasks, NSPDI-SNN consistently achieved high sparsity with minimal performance degradation. In particular, our method achieved the best experimental results on all three event stream datasets. Further analysis showed that NSPDI significantly improved the efficiency of synaptic information transfer as sparsity increased. In conclusion, our results indicate that the complex structure and nonlinear computation of neuronal dendrites provide a promising approach for developing efficient SNN methods.