Requirements classification is essential for organizing and managing software development tasks. However, in the aerospace domain, this process is especially challenging because of (i) the absence of a unified, domain-specific taxonomy, as different developers often adopt divergent classification schemes, and (ii) frequently intertwinement of functional and safety requirements driven by stringent reliability and certification standards, which leads to multi-label classifications. Collectively, these factors render manual classification costly, error-prone, and inconsistent. Existing supervised classifiers highly rely on large annotated datasets, while LLM-based methods struggle with multi-label predictions across large, hierarchical label spaces. To address these challenges, in this paper, we propose a novel taxonomy-guided classification approach, named TRClass, for aerospace requirements. The key idea behind TRClass is to integrate domain knowledge into the classification process by first constructing a unified taxonomy in a semi-automated way, which extracts structure from existing documents and then refines it with expert validation. TRClass then guides an LLM to classify new requirements by reasoning step-by-step through the taxonomy hierarchy, using few-shot retrieval and confidence-based exploration to support accurate multi-label decisions. We evaluate TRClass on a self-constructed industrial aerospace dataset, which consists of 1,752 requirements organized into a 4-level taxonomy. Results show that TRClass achieves 79% precision and 82% recall, outperforming state-of-the-art baselines by 32–65% in F1 score. A user study further reveals that 74% of TRClass’s classifications are correct and usable without any human revision, highlighting its practical effectiveness in applying domain knowledge to LLM-based requirements classification.