Memory-safety attacks have been one of the most critical threats against computing systems. Although a wide-range of defense techniques have been developed against these attacks, the existing mitigation strategies have several limitations. In particular, most of the existing mitigation approaches are based on aborting or restarting the victim program when a memory-safety attack is detected, thus making the system unavailable. This might not be acceptable in systems with stringent timing constraints, such as cyber-physical systems (CPS), since the system unavailability leaves the control system in an unsafe state. To address this problem, we propose CIMA -- a resilient and light-weight mitigation technique that prevents invalid memory accesses at runtime. CIMA manipulates the compiler-generated control flow graph to automatically detect and bypass unsafe memory accesses at runtime, thereby mitigating memory-safety attacks along the process. An appealing feature of CIMA is that it also ensures system availability and resilience of the CPS even under the presence of memory-safety attacks. To this end, we design our experimental setup based on a realistic Secure Water Treatment (SWaT) and Secure Urban Transportation System (SecUTS) testbeds and evaluate the effectiveness and the efficiency of our approach. The experimental results reveal that CIMA handles memory-safety attacks effectively with low overhead. Moreover, it meets the real-time constraints and physical-state resiliency of the CPS under test.