Federated fine-tuning enables privacy-preserving Large Language Model (LLM) adaptation, but its high memory cost limits participation from resource-constrained devices. We propose FedPruner, an innovative federated fine-tuning paradigm that tackles this via intelligent layer pruning. FedPruner flexibly prunes the global model, creating personalized submodels based on device memory constraints. It employs a macro-micro synergistic pruning framework: a macro-level functionality-driven layer orchestration mechanism groups layers, while a micro-level importance-aware layer selection strategy prunes within groups to build device-specific submodels. We further introduce a fine-grained variant that independently prunes Multi-Head Attention and Feed-Forward Network components to precisely preserve critical architectural elements. Extensive experimental results demonstrate that FedPruner significantly outperforms state-of-the-art approaches, achieving up to a 1.98\% improvement in average model accuracy while reducing peak memory usage by 75\%.