With the advancements in utilizing Artificial Intelligence (AI) in embedded safety-critical systems based on Field-Programmable Gate Arrays (FPGAs), assuring that these systems meet their safety requirements is of paramount importance for their revenue service. Based on this context, this paper has two main objectives. The first of them is to present the Safety ArtISt method, developed by the authors to guide the lifecycle of AI-based safety-critical systems, and emphasize its FPGA-oriented tasks and recommended practice towards safety assurance. The second one is to illustrate the application of Safety ArtISt with an FPGA-based braking control system for autonomous vehicles relying on explainable AI generated with High-Level Synthesis. The results indicate that Safety ArtISt played four main roles in the safety lifecycle of AI-based systems for FPGAs. Firstly, it provided guidance in identifying the safety-critical role of activities such as sensitivity analyses for numeric representation and FPGA dimensioning to achieve safety. Furthermore, it allowed building qualitative and quantitative safety arguments from analyses and physical experimentation with actual FPGAs. It also allowed the early detection of safety issues—thus reducing project costs—and, ultimately, it uncovered relevant challenges not discussed in detail when designing safety-critical, explainable AI for FPGAs.