GraphQL data fetching with SWR React Hooks and Hasura involves utilizing SWR, a stale-while-revalidate caching strategy, to efficiently manage data fetching and revalidation. By using SWR, developers can first return cached data and then fetch updated data, ensuring efficient data handling. The SWR API allows for simple integration with GraphQL, using a key to identify requests and an async fetcher function to retrieve data, with a focus on preventing duplicate requests across components. The integration with Hasura Cloud facilitates the creation of a GraphQL API, enabling developers to easily deploy and manage a database, and demonstrates the use of SWR hooks, such as useSWR and mutate, for handling queries and mutations. Developers can perform GraphQL queries, mutations, and subscriptions, utilizing native HTTP and WebSocket connections, while also accommodating server-side pre-rendering for SEO benefits using initialData and getStaticProps. The process includes setting up a Hasura deployment, creating database tables, and implementing frontend data fetching, with the source code available for further exploration and experimentation.