Heart rate variability (HRV), as measured by ultra-wideband (UWB) radar, enables contactless monitoring of physiological functioning in the human body. In the current study, we verified the reliability of HRV extraction from radar data, under limited transmitter power. In addition, we conducted a feasibility study of mental state classification from HRV data, measured using radar. Specifically, arctangent demodulation with calibration and low rank approximation have been used for radar signal pre-processing. An adaptive continuous wavelet filter and moving average filter were utilized for HRV extraction. For the mental state classification task, performance of support vector machine, k-nearest neighbors and random forest classifiers have been compared. The developed system has been validated on human participants, with 10 participants for HRV extraction, and three participants for the proof-of-concept mental state classification study. The results of HRV extraction demonstrate the reliability of time-domain parameter extraction from radar data. However, frequency-domain HRV parameters proved to be unreliable under low SNR. The best average overall mental state classification accuracy achieved was 82.34%, which has important implications for the feasibility of mental health monitoring using UWB radar.