Frequency modulated continuous wave (FMCW) millimeter-wave (mmWave) radars play a critical role in many of the advanced driver assistance systems (ADAS) featured on today's vehicles. While previous works have demonstrated (only) successful false-positive spoofing attacks against these sensors, all but one assumed that an attacker had the runtime knowledge of the victim radar's configuration. In this work, we introduce MadRadar, a general black-box radar attack framework for automotive mmWave FMCW radars capable of estimating the victim radar's configuration in real-time, and then executing an attack based on the estimates. We evaluate the impact of such attacks maliciously manipulating a victim radar's point cloud, and show the novel ability to effectively `add' (i.e., false positive attacks), `remove' (i.e., false negative attacks), or `move' (i.e., translation attacks) object detections from a victim vehicle's scene. Finally, we experimentally demonstrate the feasibility of our attacks on real-world case studies performed using a real-time physical prototype on a software-defined radio platform.