Strong shock waves generated during the pyrotechnic separation process of aerospace vehicles can cause high-frequency damage or even structural failure to the vehicle’s structure. Existing structural designs for shock attenuation typically rely on shock response spectra methods, which require multiple finite element calculations to determine the optimal geometric parameters, leading to relatively low efficiency. In this work, we propose a spectral response prediction method for spacecraft structures using the Deep Operator Network (DeepONet). This method preserves the physical relationships between input variables, modularizes geometric and positional input data, and outputs the spectral response. We integrate this neural model to analyze the impact of spacecraft structural parameters on shock resistance performance, revealing that circumferential reinforcement has the most significant influence on shock resistance. Then, we conduct a detailed analysis of the DeepONet model, noting that models with a higher number of neurons per layer train more quickly but are prone to overfitting. Additionally, we find that focusing on specific frequency bands for spectral response prediction yields more accurate results.