P-type point contact (PPC) HPGe detectors are a leading technology for rare event searches due to their excellent energy resolution, low thresholds, and multi-site event rejection capabilities. We have characterized a PPC detector’s response to α particles incident on the sensitive passivated and p+ surfaces, a previously poorly-understood source of background. The detector studied is identical to those in the Majorana Demonstrator experiment, a search for neutrinoless double-beta decay (0νββ) in 76Ge. α decays on most of the passivated surface exhibit significant energy loss due to charge trapping, with waveforms exhibiting a delayed charge recovery (DCR) signature caused by the slow collection of a fraction of the trapped charge. The DCR is found to be complementary to existing methods of α identification, reliably identifying α background events on the passivated surface of the detector. We demonstrate effective rejection of all surface α events (to within statistical uncertainty) with a loss of only 0.2% of bulk events by combining the DCR discriminator with previously-used methods. The DCR discriminator has been used to reduce the background rate in the 0νββ region of interest window by an order of magnitude in the Majorana Demonstrator and will be used in the upcoming LEGEND-200 experiment.