High-resolution range profile (HRRP) sequences have great potential for space target classification because they can provide both scattering information and micromotion information. However, many factors cause an obtained HRRP sequence for a space target to be corrupted in real cases due to noise interference, limited radar resources, and the requirement of multitarget observations. Many space target classification methods cease to be effective when HRRP sequences are corrupted, so classifying space targets with corrupted HRRP sequences is still a challenging problem. To solve this problem, a novel space target classification method based on a temporal–spatial feature aggregation network (TSFA-Net) is proposed by using the corrupted HRRP sequences directly. First, a sequence-to-token module (S2T-module) is designed to extract low-level and fine-grained features from the raw inputs. Second, to effectively model the long-range dependencies among corrupted HRRP sequences and capture global representations without losing target local features, we propose a parallel and dual-branch block, i.e., a temporal–spatial feature aggregation block (TSFA-block), by combining a Transformer network and a convolutional neural network (CNN). Then, via progressively hierarchically stacking TSFA-blocks, a hierarchical temporal–spatial feature aggregation subnetwork (H-TSFA-subnetwork) is constructed to obtain the final temporal–spatial features. Finally, a token-to-label module (T2L-module) is adopted to obtain the classification results. Extensive experiments demonstrate that the proposed method achieves state-of-the-art classification accuracy for space target classification with HRRP sequences, especially under the conditions of a low signal-to-noise ratio and a high missing rate.