GraphQL mutations can present several challenges in API design, but adhering to certain principles, such as those outlined in Facebook's Relay API spec, can mitigate these issues. Key practices include using a unique output type with a suffix like "Payload" for each mutation, which allows for flexibility in expanding response fields without affecting existing structures. Similarly, employing a single, unique input type, known as the Parameter Object Pattern, simplifies code maintenance as mutations grow in complexity. The spec also introduces the concept of idempotent mutations through a parameter called "clientMutationId," which helps avoid duplicate requests by caching responses based on this identifier. Additionally, naming conventions suggest using verbs for mutation names to clearly indicate action. Relay's standardized approach is widely supported by GraphQL libraries, facilitating easy implementation while ensuring that mutations remain robust and adaptable as APIs evolve.