We present high-resolution (12''-24'')12CO(J = 2-1),13CO(2-1), CS(2-1), CS(3-2), and CS(5-4) maps of the central 4' × 4' of Mon R2 and study the bipolar outflow, the dense core, and their mutual interaction. The high-velocity 12CO and 13CO emissions that trace the bipolar outflow show that the outflow lobes are limb-brightened shells of accelerated gas that have the Mon R2 IR cluster near their apex and extend approximately toward the north and south. These shells of gas are clumpy, and their emission at the highest velocities arises from discrete condensations that move with the flow but each has a slightly different speed. The CS data, on the other hand, trace the ambient core at low velocities, but also trace the accelerated gas of the outflow at higher speeds. The ambient CS emission shows that the core has a cavity along the path of the outflow, and that the walls of this cavity coincide in position and orientation with the shells of the bipolar flow. The accelerated CS emission concentrates along the cavity walls and arises from the same clumpy shells of gas that form the outflow lobes in 12CO and 13CO. This outflow material, therefore, is rather dense, and a solution of the CS radiative transfer shows that it is as dense as the gas in the core (≈ 4 × 105 cm-3), suggesting that what we see as outflow is in fact gas from the dense core that has been set into motion. With the same radiative transfer analysis of the CS lines, we estimate that from a total of 1000 M☉ of dense gas in the core, more than 170 M☉ have been accelerated and incorporated into the bipolar flow. In addition, the CS spectra show a systematic enhancement of the line width toward the IR cluster that suggests the outflow has increased the gas turbulence in its vicinity. The amount of kinetic energy contained in both the bipolar and turbulent motions is comparable to the total binding energy of the dense gas, and this shows that the action of the outflow on the core can be strong enough to affect the distribution of dense gas in the core. We therefore propose that the cavity in the dense gas is the result of the evacuation of a channel by the outflow, and that the material initially filling its volume has been accelerated and incorporated into the flow. The Mon R2 system, therefore, illustrates how bipolar molecular outflows form through the acceleration of ambient molecular gas and that the process of molecular outflow formation is accompanied by a partial destruction of the dense gas environment of the newly formed star.