Dominant approaches to Knowledge Base Question Answering (KBQA) fall into two categories. First is the generation of a formal query that suffers from brittleness and limited explainability, and the second is direct answer retrieval through KB exploration that is computationally costly and prone to hallucination. To combine the strengths of both paradigms while mitigating their respective weaknesses, we introduce DeSQ (Decomposition-based SPARQL Query Generation), a KB-agnostic framework that operates in three stages. First, it decomposes complex questions into Atomic Constraints (ACs) that mirror the relational structure of the underlying KB. Second, it generates a two-part structured output: (a) Mapping of each AC to its corresponding SPARQL Fragment, using standardized variable and URIs placeholders, and (b) URIs Grounding block describing each placeholder. Third, it assembles these fragments into a complete SPARQL query. DeSQ surpasses state-of-the-art approaches on four out of five major benchmarks and demonstrates superior robustness to lexical variation. Beyond performance gains, our framework greatly simplifies evaluation by eliminating the need for a live KB endpoint, and its structured output enables fine-grained error analysis, allowing more targeted interventions for improvement.