Previous literature has compared the performance of existing ground point classification (GPC) techniques on airborne LiDAR (ALS) data (LiDAR—light detection and ranging); however, their performance when applied to terrestrial LiDAR (TLS) data has not yet been addressed. This research tested the classification accuracy of five openly-available GPC algorithms on seven TLS datasets: Zhang et al.’s inverted cloth simulation (CSF), Kraus and Pfeiffer’s hierarchical weighted robust interpolation classifier (HWRI), Axelsson’s progressive TIN densification filter (TIN), Evans and Hudak’s multiscale curvature classification (MCC), and Vosselman’s modified slope-based filter (MSBF). Classification performance was analyzed using the kappa index of agreement (KIA) and rasterized spatial distribution of classification accuracy datasets generated through comparisons with manually classified reference datasets. The results identified a decrease in classification accuracy for the CSF and HWRI classification of low vegetation, for the HWRI and MCC classifications of variably sloped terrain, for the HWRI and TIN classifications of low outlier points, and for the TIN and MSBF classifications of off-terrain (OT) points without any ground points beneath. Additionally, the results show that while no single algorithm was suitable for use on all datasets containing varying terrain characteristics and OT object types, in general, a mathematical-morphology/slope-based method outperformed other methods, reporting a kappa score of 0.902.