Continual Structured Knowledge Reasoning (CSKR) focuses on training models to handle sequential tasks, where each task involves translating natural language questions into structured queries grounded in structured knowledge. Existing general continual learning approaches face significant challenges when applied to this task, including poor generalization to heterogeneous structured knowledge and inefficient reasoning due to parameter growth as tasks increase. To address these limitations, we propose a novel CSKR framework, \textsc{K-DeCore}, which operates with a fixed number of tunable parameters. Unlike prior methods, \textsc{K-DeCore} introduces a knowledge decoupling mechanism that disentangles the reasoning process into task-specific and task-agnostic stages, effectively bridging the gaps across diverse tasks. Building on this foundation, \textsc{K-DeCore} integrates a dual-perspective memory consolidation mechanism for distinct stages and introduces a structure-guided pseudo-data synthesis strategy to further enhance the model's generalization capabilities. Extensive experiments on four benchmark datasets demonstrate the superiority of \textsc{K-DeCore} over existing continual learning methods across multiple metrics, leveraging various backbone large language models.