Heart rate (HR) monitoring is crucial for assessing physical fitness, cardiovascular health, and stress management. Millimeter-wave radar offers a promising noncontact solution for long-term monitoring. However, accurate HR estimation remains challenging in low signal-tonoise ratio (SNR) conditions. To deal with both respiration harmonics and intermodulation interference, this paper proposes a cancellation-before-estimation strategy. Firstly, we present the adaptive extensive cancellation algorithm (ECA) to suppress respiratory and its low-order harmonics. Then, we propose an adaptive harmonic enhanced trace (AHET) method to avoid intermodulation interference by refining the HR search region. Various experimental results validate the effectiveness of the proposed methods, demonstrating improvements in accuracy, robustness, and computational efficiency compared to conventional approaches based on the FMCW (Frequency Modulated Continuous Wave) system