Existing LLM-based molecular optimization methods frame the task as molecule-to-molecule mapping, forcing models to implicitly learn structure-property relationships from paired SMILES alone. We argue this misses a key ingredient: task-level chemical knowledge that tells the model which structural motifs to prefer or avoid for a given property direction, before it ever looks at a specific molecule. We propose SkillMol, which constructs compact task skills – sets of recommended and discouraged structural motifs for each optimization objective – from domain knowledge, and pairs them with an atom-anchored action interface that decomposes editing into discrete, executable operations. Skills are used twice: as explicit training context so the model learns skill-conditioned edit actions, and as functional-group constraints during inference search. A deterministic RDKit executor applies the proposed graph edits. On the MoleculeSTM benchmark across 14 molecular editing tasks, SkillMol achieves 92.5% loose and 80.0% strict hit ratio on single-property tasks and 65.3% average across loose and strict multi-property columns, outperforming strong LLM baselines. Our code can be found at https://github.com/jiajunyu1999/SkillMol.