The aerospace and automotive industries demand the development of new manufacturing processes. The productivity during machining of very flexible aerospace and automotive aluminum components is limited for self-excited vibrations. New solutions are needed to suppress vibrations that affect the accuracy and quality of the machined surfaces. Rejection of one piece implies an increase in the manufacturing cost and time. This paper is focused on the design, manufacturing and characterization of a magnetorheological damper. The damper was attached to a thin-floored component and a magnetic field was controlled in order to modify the damping behavior of the system. The dynamics of the machining process was developed by considering a three-degree-of-freedom model. This study was experimentally validated with a bull-nose end milling tool to manufacture monolithic parts with thin wall and thin floor. Experimental tests and characterization of the magnetorheological damper permitted to improve the surface finish and productivity during the machining of thin-floored components. A further aim of this paper was to develop a rheological damper by using magnetorheological fluids (MR) to change the thin floor rigidity with voltage. The stability of the milling process was also analytically described considering one, two or three degrees of freedom, using a mathematical integration model based on the Enhanced Multistage Homotopy Perturbation Method (EMHPM).