A method resumes an interrupted process for sawing a workpiece into wafers using a wire saw that includes advancing a wire web into existing sawing kerfs of the workpiece with a forward movement of the sawing wire with a first speed in the presence of a liquid sawing medium until the wire web or workpiece has reached a position corresponding to the interruption of the wire sawing process. The sawing wire is moved in defined time intervals by a forward movement of a particular length with a second speed and a backward movement of another length with a third speed, where the backward length is less than the forward length and the forward and backward movement correspond to a cycle. The wire length that is unwound during the forward movements is increased until the length during the forward movement corresponds to the length of the forward movement before the interruption.