Modern Mixture-of-Experts (MoE) models increasingly rely on large-scale AI accelerator clusters for efficient training. Ascend NPUs expose heterogeneous on-chip compute resources, including matrix-oriented AIC units and vector-oriented AIV units with explicit cross-queue synchronization support. However, existing training frameworks largely execute MoE operators in a serialized kernel-by-kernel manner, leaving substantial heterogeneous parallelism underutilized. This paper presents HyperParallel-MoE, a compilation and scheduling framework for MoE training on Ascend NPUs. HyperParallel-MoE transforms operator-level MoE execution into a statically scheduled tile-level heterogeneous taskflow spanning AIC and AIV resources. It introduces AIV-driven one-sided communication to eliminate host-side collective synchronization, dependency-preserving tile task generation to unify communication and computation under a common task abstraction, and event-driven static scheduling to coordinate cross-queue execution with low runtime overhead. HyperParallel-MoE further executes the compiled taskflow within a unified runtime that concurrently drives AIC and AIV workers inside a single kernel launch, enabling fine-grained overlap among communication, matrix computation, and vector computation while preserving existing optimized operators. We implement HyperParallel-MoE in the MindSpore and MindFormers stack and evaluate it using DeepSeek-style MoE models on Ascend A3 clusters. Across multiple expert-parallel configurations, HyperParallel-MoE reduces Dispatch-to-Combine MoE-FFN latency by up to 1.58x, demonstrating that tile-level heterogeneous scheduling can substantially improve MoE training efficiency on modern NPUs. The source code is available at https://gitcode.com/mindspore/hyper-parallel/tree/master/hyper_parallel/core/multicore