In response to the low soil breakage rate and poor flatness of current combined soil preparation equipment for growing potatoes under the clay loam conditions of Northeast China, this paper presents the design of an arc-shaped tooth press device for such equipment, describing its overall structure and working principle. By conducting force analysis on the press roller and shear stress analysis with MATLAB, we obtained the structural parameters and the corresponding value ranges impacting the operational effectiveness of the press device. A three-factor, five-level quadratic regression orthogonal rotational combination test was carried out using EDEM discrete element simulation software, taking the soil breakage rate and flatness as the test indicators. The forward speed, roller tooth arc length, and angle between the roller tooth and the vertical direction (ABRTVD) were the test factors. Design-Expert 8.0.6 software was used for data processing and analysis, and the results showed that the optimal parameter combination consisted of a forward speed of 0.72~1.15 m·s−1, a roller tooth arc length of 58.7 mm, and an ABRTVD of 37.74°, at which point the soil breakage rate was 93.58% and the flatness value was 21.36 mm. The optimal combination of parameters was selected for the field test, resulting in a soil breakage rate of 95.6% and a flatness value of 20.6 mm. The results of the simulation test were found to be consistent with the field test results, thus validating the efficacy of the device design. The findings of this study can provide a reference for enhancing the operational performance of combined soil preparation equipment for growing potatoes under clay loam conditions.