Button cutters are the main cutting tools used in Raise Boring Machines (RBMs), particularly in very hard and abrasive ground conditions where their longer lifespan makes them preferable to other types of cutters. Meanwhile, single-disc cutters are the most efficient hard rock cutters and are frequently utilized in Tunnel Boring Machines. Although it is challenging to conduct full-scale linear cutting tests with multi-row button cutters due to laboratory equipment limitations and there are almost none of theoretical and empirical approaches to predict their cutting performances, it is very common and easier to generate data for single-disc cutters by cutting tests or using theoretical or statistical methods. By establishing statistical relationships between experimental cutting performances of button and disc cutters, it may be possible to compare the cutting performance of these roller-type cutters and transition from disc cutter performance to button cutter performance without conducting very difficult cutting tests with button cutters. The basic aim of this study is to investigate correlations between performances of a single-kerf button cutter and a constant-cross-section single-disc cutter. Full-scale linear cutting tests are performed on five different block rock samples with a 305-mm (12 inch)-diameter button cutter having an insert tip width of 11 mm in single- and double-spiral cutting patterns (pitch of 15 mm). Additionally, a series of single-spiral cutting pattern tests are performed on the same block samples with a 330-mm (13 inch)-diameter disc cutter having a tip width of 12 mm. The results indicate that optimum cutting parameters of the button cutter (normal and rolling forces, and coarseness index normalized by depth of cut per revolution, specific energy, and ratio of line spacing to depth of cut per revolution) can be predicted from the optimum cutting parameters of the disc cutter. The correlations are reliably used for predicting field performance of an RBM, which generally validates the approach used in this study. The study also provides a set of relationships between the cutting performance parameters of the disc cutter and the physical–mechanical properties of the rock samples. The relationships obtained in this study can be used for the purpose of predicting field performances of mechanical miners using button and disc cutters.