Recent advancements in Ultra-Wideband (UWB) radar technology have enabled contactless, non-line-of-sight vital sign monitoring, making it a valuable tool for healthcare. However, UWB radar's ability to capture sensitive physiological data, even through walls, raises significant privacy concerns, particularly in human-robot interactions and autonomous systems that rely on radar for sensing human presence and physiological functions. In this paper, we present Anti-Sensing, a novel defense mechanism designed to prevent unauthorized radar-based sensing. Our approach introduces physically realizable perturbations, such as oscillatory motion from wearable devices, to disrupt radar sensing by mimicking natural cardiac motion, thereby misleading heart rate (HR) estimations. We develop a gradient-based algorithm to optimize the frequency and spatial amplitude of these oscillations for maximal disruption while ensuring physiological plausibility. Through both simulations and real-world experiments with radar data and neural network-based HR sensing models, we demonstrate the effectiveness of Anti-Sensing in significantly degrading model accuracy, offering a practical solution for privacy preservation.