We focus on the subaperture polishing tool concept development for suppressing midspatial frequencies (MSF) arising from computer numerical control machining of aspherical optical surfaces. The selective effect in the MSF range is achieved by setting the tool viscoelastic properties so that rigidity increases in the frequency-domain generated by the rotational tool movement over the aspheric surface with the MSF while the tool remains flexible in the lower frequency range associated with tool radial direction movement. The mechanism of MSF removal is discussed in detail, including in terms of elasticity module frequency dependences, and is also experimentally verified. In order to monitor and optimize viscoelastic properties, especially in regard to frequency dependences, the dynamic mechanical analysis method has been developed and applied and is presented in the paper as well.