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Relaxation dynamics in nonlinear response regime have become an emerging novel tool to study the dynamics and structure of glassy materials. It provides additional insights relative to the standard linear response experiments. However, limited by inherent endurance of the materials to external fields, up to now, almost all the probed nonlinear effects are very weak. Here, strong nonlinear effects are observed in magnetic systems with disordered spins (i.e. magnetic glass). In particular, we report a pronounced fragility transition as driven by the external magnetic field as a result of nonlinear dynamic response. Such model systems provide a new platform to study the glassy dynamics with large and tunable nonlinearity.