The MAJORANA DEMONSTRATOR is searching for neutrinoless double-beta decay in 76Ge using arrays of point-contact germanium detectors operating at the Sanford Underground Research Facility. Background results in the neutrinoless double-beta decay region of interest from data taken during construction, commissioning, and the start of full operations have been recently published. A pulse shape analysis cut applied to achieve this result, named AvsE, is described in this paper. This cut is developed to remove events whose waveforms are typical of multi-site energy deposits while retaining (90 +/- 3.5)% of single-site events. This pulse shape discrimination is based on the relationship between the maximum current and energy, and tuned using 228Th calibration source data. The efficiency uncertainty accounts for variation across detectors, energy, and time, as well as for the position distribution difference between calibration and $0 ubetabeta$ events, established using simulations.
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