Question answering on free-form tables (TableQA) is challenging due to the absence of predefined schemas and the presence of noise in large tables. While Large Language Models (LLMs) have shown promise in TableQA, they struggle with large free-form tables and noise sensitivity. To address these challenges, we propose TabSD, a SQL-based decomposition model that enhances LLMs' ability to process large free-form tables. TabSD generates SQL queries to guide the table decomposition, remove noise, and processes sub-tables for better answer generation. Additionally, SQL Verifier refines SQL outputs to enhance decomposition accuracy. We introduce two TableQA datasets with large free-form tables, SLQA and SEQA, which consist solely of large free-form tables and will be publicly available. Experimental results on four benchmark datasets demonstrate that TABSD outperforms the best-existing baseline models by 23.07%, 2.84%, 23.24% and 9.32% in accuracy, respectively, highlighting its effectiveness in handling large and noisy free-form tables.