Due to recent cyber attacks on various cyber-physical systems (CPSes), traditional isolation based security schemes in the critical systems are insufficient to deal with the smart adversaries in CPSes with advanced information and communication technologies (ICTs). In this paper, we develop real-time assessment and mitigation of an attack's impact as a system's built-in mechanisms. We study a general class of attacks, which we call time delay attack, that delays the transmissions of control data packets in the CPS control loops. Based on a joint stability-safety criterion, we propose the attack impact assessment consisting of (i) a machine learning (ML) based safety classification, and (ii) a tandem stability-safety classification that exploits a basic relationship between stability and safety, namely that an unstable system must be unsafe whereas a stable system may not be safe. In this assessment approach, the ML addresses a state explosion problem in the safety classification, whereas the tandem structure reduces false negatives in detecting unsafety arising from imperfect ML. We apply our approach to assess the impact of the attack on power grid automatic generation control, and accordingly develop a two-tiered mitigation that tunes the control gain automatically to restore safety where necessary and shed load only if the tuning is insufficient. We also apply our attack impact assessment approach to a thermal power plant control system consisting of two PID control loops. A mitigation approach by tuning the PID controller is also proposed. Extensive simulations based on a 37-bus system model and a thermal power plant control system are conducted to evaluate the effectiveness of our assessment and mitigation approaches.