Enterprises, public organizations, and localization providers increasingly rely on Document-level Machine Translation (DocMT) to process contracts, reports, manuals, and multimedia transcripts across languages. However, existing MT systems often struggle to handle discourse-level phenomena such as pronoun resolution, lexical cohesion, and ellipsis, resulting in inconsistent or incoherent translations. We propose **GRAFT**, a modular graph-based DocMT framework that leverages Large Language Model (LLM) agents to segment documents into discourse units, infer inter-discourse dependencies, extract structured memory, and generate context-aware translations. GRAFT transforms documents into directed acyclic graphs (DAGs) to explicitly model translation flow and discourse structure. Experiments across eight language directions and six domains show GRAFT outperforms commercial systems (e.g., Google Translate) and closed LLMs (e.g., GPT-4) by an average of 2.8 d-BLEU, and improves terminology consistency and discourse handling. GRAFT supports deployment with open-source LLMs (e.g., LLaMA, Qwen), making it cost-effective and privacy-preserving. These results position GRAFT as a robust solution for scalable, document-level translation in real-world applications.