A computer-implemented technique is described herein for facilitating a user's interaction with digital content in a mixed reality environment. The technique involves: displaying digital content to the user in a mixed reality environment in one or more two-dimensional graphical pages, via a display device of a mixed reality device; receiving input information from one or more environment-sensing devices that capture movement of the user; and detecting, based on the input information, whether the user has performed a telltale gesture directed to a graphical page. Each such telltale gesture includes physical action(s) that a user might perform on a physical object, such as a physical piece of paper. If the gesture-detecting engine detects such a gesture, the technique updates the display device of the mixed reality device to show an appropriate outcome. The telltale gestures include a part-removing gesture, a moving gesture, and a page-flipping gesture, etc.