This paper proposes a framework for processing the B-scans of tree trunks and revealing the presence of trees' internal defects (i.e., cavities and decays) from the signatures of their reflections. The framework uses the B-scans obtained by a standoff step frequency continuous wave radar system, moved in straight trajectories at a standoff distance facing the tree trunks' surfaces. In particular, the proposed framework first applies an antenna calibration to the raw B-scans to suppress the antenna's internal reflections. Then, it leverages a column-connection clustering (C3) algorithm to remove the signatures of the reflections from the trunk surface. Finally, it applies a Kaiser window to the Fourier-transformed A-scans of the processed B-scan to further increase the signal-to-noise ratio (SNR). The application of the proposed framework to measured (raw) B-scans shows that the proposed framework improves the SNR by more than 30 dB and reveals the signatures of the defects in the B-scans. The proposed framework can be used for many other standoff radar applications, such as through-the-wall imaging, defect/anomaly detection in concrete walls, in which the magnitude of the reflection from the main target is two/three orders smaller than the magnitude of the unwanted reflections from the surfaces or other objects.