As large neural network models (e.g., LLMs) grow in scale, single-cluster resources become insufficient, making cross-cluster distributed training essential. Cross-cluster training is challenging: hardware heterogeneity complicates load balancing and parallelization strategy and introduces hardware compatibility issues in implementation; cross-cluster communication bottlenecks severely impact training throughput. We present HetAuto, an automatic parallelization system for efficient cross-cluster heterogeneous large model training. HetAuto contributes three key innovations: (1) a principle-guided MCTS algorithm with a random forest-enhanced cost model that efficiently searches parallelization strategies and quickly evaluates their performance under heterogeneous configurations; (2) cross-cluster communication optimizations including Virtual-1F1B scheduling that overlaps communication with computation and an optimized resharding strategy for inter-stage communication; and (3) a unified API enabling seamless integration of diverse accelerators. We evaluate HetAuto across 4 different clusters with up to 736 heterogeneous devices. The evaluation results show that HetAuto achieves up to 1.57× training throughput improvement over representative baselines, and strikes an efficient balance between solution quality and search overhead.