In the drilling of stacked materials, burrs produced on both the surface layer and the interlayer have some undesirable characters with regard to assembly quality, and deburring is a time consuming and costly operation. This paper presented an experimental study on the dry drilling of Ti-6Al-4V titanium alloy and 7075-T6 aluminum alloy stacked materials, which was performed by using uncoated cemented carbide drills. The burr size was evaluated at various spindle speeds, feed rates, stacking sequences, and clamp forces. After which, the burr morphology was observed and analyzed. Finally, a new multi-objective optimization algorithm, which was derived from the game theory, was used to select optimum process parameters to minimize burr size. The best process parameters recorded in this paper were at the spindle speed of 2,000 r/min, the feed rate of 0.075 mm/r, the pressure of 0.3 MPa, and the stacking sequence of the Ti-6Al-4V titanium alloy on top of the 7075-T6 aluminum alloy.