When the Rotary Cutting Drum for mining Cobalt-rich Crust is working on the fluctuant microtopography of sea floor, it's necessary to determine the cutting depth according to the mining requirement. In this paper, the mathematic model is established for determining the cutting depth and position-pose, namely the optimal cutting position-pose of the Rotary Cutting Drum, and the mathematic solution and the simplified solution are both provided. The modeling and its analysis in this paper will supply some important references to detecting the depth of the cobalt-rich crust and the fluctuant microtopography of the cobalt crust.