The Majorana Demonstrator is searching for neutrinoless double-beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) in $^{76}\mathrm{Ge}$ using arrays of point-contact germanium detectors operating at the Sanford Underground Research Facility. Background results in the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ 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 multisite energy deposits while retaining $(90\ifmmode\pm\else\textpm\fi{}3.5)%$ of single-site events. This pulse shape discrimination is based on the relationship between the maximum current and energy, and tuned using $^{228}\mathrm{Th}$ 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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ events, established using simulations.