The emergency collision avoidance capabilities of autonomous vehicles (AVs) are crucial for enhancing their active safety performance, particularly in extreme scenarios where standard methods fall short. This study introduces an Extreme Maneuver Controller (EMC) for AVs, utilizing reachability-guided reinforcement learning (RL) to address these challenging situations. By applying pseudospectral methods, we solve the minimum backward reachable tube (Min-BRT) to identify regions where conventional avoidance maneuvers are infeasible, establishing a theoretical basis for triggering extreme maneuvers. A novel controller, employing reachability-guided RL, enables vehicles to execute extreme maneuvers to escape these critical regions. During training, the value function derived from the Min-BRT solution informs the initialization of the Critic networks, enhancing training efficiency. Real-world scenario-based experimental results with actual vehicles validate that the proposed policy, effectively executes beyond-the-limit maneuvers, mitigating collision risks under emergency condition. Furthermore, these extreme maneuvers are executed with minimal deviation from the original driving objectives, ensuring a smooth and stable transition upon completion of extreme maneuvers.