Circular samples made of rubber-like material, can be cut out using custom cookie cutter tool. This latter acts as a spinning disk cutter and create cylinder of specified diameters with little waste. Examples of such a cutter are described in [1] and reported in the figure below.
It can be rotated using a driller or a milling machine. The rotation and downward speeds have to be properly chosen as a function of the material not to induce residual stresses when cutting. We usually fix the sheet or pad with double sided tape on a flat plate to make sure the circular samples stay at the same place during the cutting process.