Low earth orbit (LEO) satellite networks are a critical component of the new generation of integrated space-terrestrial collaborative networks, providing high-speed internet services to global users. However, these networks face numerous security challenges. Due to the collaborative dependencies among LEO satellites, a few satellite failures may trigger cascading failures, leading to network-wide disruptions. Therefore, investigating network robustness under cascading failures is essential. To address the challenge of robustness assessment for multi-layer LEO satellite networks during cascading failures, this paper proposes a dynamic heterogeneous cascading failure model. Specifically, beyond simulating orbital dynamics and dynamic network topologies, the model introduces novel designs: firstly, a dynamic load model capturing the spatiotemporal imbalance in global user load distribution; secondly, a multi-layer heterogeneous capacity model accounting for satellite iterative upgrades during constellation scaling, while explicitly addressing node heterogeneity across orbital layers. Based on the cascading failure model, simulations of LEO satellite networks with varying parameters demonstrate the significant impact of network characteristics and model-related parameters on robustness. This model and its associated results provide practical insights for mitigating cascading risks and enhancing the robustness of LEO satellite networks.