A digital elevation model (DEM) is an essential element of input data in the model research of watersheds. Recently, progress in measurement techniques has led to the availability of such data with high spatial resolution. Therefore, simplification of DEMs to shorten the time of their processing is a significant, but insufficiently investigated issue. This study, gradually and with various methods, carried out a great simplification of a detailed LiDAR-derived DEM. Then, the impact of that treatment on the precision of the selected elements for modeling a watershed was assessed. The simplification comprised a reduction in resolution, with the use of statistical resampling methods, namely giving an average, modal, median, minimum, maximum, or the closest value to the pixels. This process was carried out in a wide range of pixel sizes, increasing by 50% each time (from 1 m to 1.5, 2.3, 3.4, 5.1, 7.6, 11, 17, 26, 38, 58, and 86 m, respectively). The precision of the obtained DEMs and the precision of the delineation of boundaries of the watershed and watercourses were assessed. With the systematic reduction in the resolution of a DEM, its precision systematically decreased. The changes in the precision of determining the watercourses and boundaries of a watershed were irregular, ranging from being very small, to mild, to significant. A method of giving the minimum value, that was simple with regard to computing, was singled out. In the determination of both the watercourses and the boundaries of a watershed, this method produced one of the best results for the higher resolution and for the lower resolution—considerably better than the other methods tested. The research was conducted on a flat agricultural catchment, and it can be assumed that the obtained conclusions can be considered for similar cases. For catchments with different characteristics, further research is advisable.