We employ a 77-81 GHz frequency-modulated continuous-wave (FMCW) millimeter-wave radar to sense anomalous vibrations during vehicle transport at highway speeds for the first time. Secure metallic containers can be breached during transport by means of drilling into their sidewalls but detecting a drilling signature is difficult because the large vibrations of transport drown out the small vibrations of drilling. For the first time, we demonstrate that it is possible to use a non-contact millimeter-wave radar sensor to detect this micron-scale intrusive drilling while highway-speed vehicle movement shakes the container. With the millimeter-wave radar monitoring the microdoppler signature of the container's vibrating walls, we create a novel signal-processing pipeline consisting of range-angle tracking, time-frequency analysis, horizontal stripe image convolution, and principal component analysis to create a robust and powerful detection statistic to alarm if drilling is present. To support this pipeline, we develop a statistical model combining the vibrating container and the random vibrations induced by vehicle movement to explore the robustness of the sensor's detection capabilities. The presented results strongly support the inclusion of a millimeter-wave radar vibration sensor into a transport security system.