This paper focuses on the problem of mechanical vibrations induced in the cutting process of stone and marble in stone cutting machines. The study shows that the main source for these vibrations is the lateral motion of the saw blade causing friction between the side body of the blade and the stone. This periodic force induced in the cutting area is reduced passively by using elastomeric pad that isolates the base of the machine from the head and the table. Adding less than 2.5% of passive damping ratio to the isolator could slightly reduce the level of vibration on the saw blade and on the table. To reduce the propagation of these vibrations through the base into the floor, another elastomeric pad is mounted under the machine. This pad reduces the immigration of oscillations through the floor to the other places in the factory. Another solution is presented is to reduce the vibrations in the whole structure significantly by using the input force this one is controlled by the linear quadratic regulator (LQR) method. The controller has the capability to regulate the vibrations in the structure by solving the Riccati equation to compute the optimal response for the input force to perform the required tasks.