Mistakes in AI systems are inevitable, arising from both technical limitations and sociotechnical gaps. While black-boxing AI systems can make the user experience seamless, hiding the seams risks disempowering users to mitigate fallouts from AI mistakes. Instead of hiding these AI imperfections, can we leverage them to help the user? While Explainable AI (XAI) has predominantly tackled algorithmic opaqueness, we propose that seamful design can foster AI explainability by revealing and leveraging sociotechnical and infrastructural mismatches. We introduce the concept of Seamful XAI by (1) conceptually transferring "seams" to the AI context and (2) developing a design process that helps stakeholders anticipate and design with seams. We explore this process with 43 AI practitioners and real end-users, using a scenario-based co-design activity informed by real-world use cases. We found that the Seamful XAI design process helped users foresee AI harms, identify underlying reasons (seams), locate them in the AI's lifecycle, learn how to leverage seamful information to improve XAI and user agency. We share empirical insights, implications, and reflections on how this process can help practitioners anticipate and craft seams in AI, how seamfulness can improve explainability, empower end-users, and facilitate Responsible AI.