In this paper, a new horizontal-shaft roller-type cotton stalk puller was designed to address the problems of weak research on cotton stalk pulling and harvesting machines, poor agronomic adaptability, and insufficient research. First, the physical and mechanical properties of cotton stalk were experimentally studied, the cotton stalk pulling force test was conducted and the moisture content and the bending characteristics of cotton stalk were evaluated. The test results showed that cotton stalk pulling force was positively correlated with the cotton stalk diameter and the bending characteristics were positively correlated with the moisture content but were not evidently influenced by the diameter. Second, with the missed pulling rate and pull-off rate as the evaluation indexes and three independent variables, namely, forward speed, linear speed of stalk pulling rod, and rotation speed of stalk pulling roller, as the influencing factors, a 3D response surface model was established. On this basis, the lack-of-fit term P (p = 0.3650) > 0.05 of the evaluation index—missed pulling rate P1—was acquired, and the P value of pull-off rate P2 was always smaller than 0.0001. Finally, the results demonstrated that the influence of various factors on the missed pulling rate of cotton stalk is significant and followed the order forward speed > linear speed of stalk pulling rod > rotation speed of stalk pulling roller; the significance level regarding the influence on the pull-off rate followed the order rotation speed of stalk pulling roller > linear speed of stalk pulling rod > forward speed. Through the parameter optimization analysis, the optimal parameter combination was obtained which coincide with the model optimization and prediction result. The proposed method provides a basis and experimental reference for studying cotton stalk harvesting machineries.