In the natural stone sector, rock blocks are cut as a plate using block-cutting machines (BCM), and the plates are polished in the polishing machines. Energy consumption is the primary operating cost in both the cutting and polishing processes. The energy consumption of BCMs is affected by many factors, with the most influential being traverse speed. The energy efficiency of BCMs can be improved by regulating the traverse speed throughout the cutting process, and the roughness of the cut surface can be reduced by keeping the ratio between the traverse speed and peripheral speed constant as an additional benefit. This also reduces energy consumption and waste production in the polishing process. In this paper, two controllers used for the regulation of traverse and peripheral speeds are applied to a laboratory-scale BCM, one of which regulates only the traverse speed, while the other regulates both the traverse and peripheral speeds. A limped hierarchical fuzzy logic controller (LHFLC) approach is used in the design of the controllers for the first time on the BCM. In the proposed LHFLC method, the design procedure of the controller is simplified, and its memory usage, computational load, and response time are decreased. The performance of the controllers (a three-input/one-output (3I1O) FLC, 3I1O LHFLC, and a three-input/two-output (3I2O) LHFLC) was tested with cutting experiments performed on three rock samples (Bilecik Beige limestone, Uşak Green marble, and Afyon travertine), and the acquired results reveal that the proposed controllers (3I1O LHFLC and 3I2O LHFLC) are more efficient than the previous controller (3I1O FLC), with over 21%. A statistical analysis shows that to improve the energy efficiency of the BCM, the 3I1O LHFLC could be used rather than the 3I1O FLC. It is further noted that statistically, the cutting rate can be kept more constant with the 3I2O LHFLC than with the 3I1O LHFLC, meaning that the surface roughness of the plates produced by the BCM can be reduced using the 3I2O LHFLC.