Photoplethysmogram (PPG) signals are widely used for wearable electronic devices nowadays. The PPG signal is extremely sensitive to the motion artifacts (MAs) caused by the subject's movement. The detection and removal of such MAs remains a difficult problem. Due to the complicated MA signal waveforms, none of the existing techniques can lead to satisfactory results. In this paper, a new framework to identify and tailor the abrupt MAs in PPG is proposed, which consists of feature extraction, change-point detection, and MA removal. In order to achieve the optimal performance, a data-dependent frame-size determination mechanism is employed. Experiments for the heart-beat-rate-measurement application have been conducted to demonstrate the effectiveness of our proposed method, by a correct detection rate of MAs at 98% and the average heart-beat-rate tracking accuracy above 97%. On the other hand, this new framework maintains the original signal temporal structure unlike the spectrum-based approach, and it can be further applied for the calculation of blood oxygen level (SpO₂).