Can we say that hard determinism and free will are mutually exclusive by definition?
Yes. However, I respectfully disagree with Not_Here's characterization of Hard Determinism; "Hard Determinism" is used to refer to the view that endorses the following conjunction: 1) Incompatibilism about Free Will and Determinism is true and 2) Determinism is true. It follows from (1) and (2) that no one has free will. So, Hard Determinism is mutually exclusive with any view that claims people have free will (e.g. typical versions of Compatibilism/Soft Determinism and Libertarianism).