Small-molecule drugs play a critical role in cancer therapy by selectively targeting key signaling pathways that drive tumor growth. While deep learning models have advanced drug discovery, there remains a lack of generative frameworks for de novo covalent molecule design using a fragment-based approach. To address this, we propose MOFF (MOlecule generation with Functional Fragments), a reinforcement learning framework for molecule generation. MOFF is specifically designed to generate both covalent and noncovalent compounds based on functional fragments. The model leverages docking scores as reward functions and is trained using the Soft Actor-Critic algorithm. We evaluate MOFF through case studies targeting Bruton's tyrosine kinase (BTK) and the epidermal growth factor receptor (EGFR), demonstrating that MOFF can generate ligand-like molecules with favorable docking scores and drug-like properties, compared to baseline models and ChEMBL compounds. As a computational validation, molecular dynamics (MD) simulations were conducted on selected top-scoring molecules to assess potential binding stability. These results highlight MOFF as a flexible and extensible framework for fragment-based molecule generation, with the potential to support downstream applications.