To address the issues of limited one-time loading capacity, single functionality, and low automation level in existing square straw bale pickers, a large automated square straw bale pick-up-and-stack truck that integrates picking, stacking, transporting, and bundling functions has been developed, combining the technical advantages of one-time field removal and storage of bales. We innovatively designed a side-pulling traction mechanism that can realize the rapid transition between the transporting state and working state of the machine; a picking device that can complete the continuous action of forking, lifting, turning positioning, and de-forking; and a bundling device that can realize the adjustment of the attitude of square straw bales. Response surface tests were conducted on the prototype to determine the key structural and operational parameters, using the bundle completion rate and regular bale rate as evaluation indicators. Regression and significance tests were performed on the machine’s forward speed, chassis frame offset, and the ground clearance of the fork tine to determine the influence and priority of these factors on the evaluation indicators. Through multi-objective function optimization of the regression model, the optimal parameter combination was found to be a machine forward speed of 15.5 km/h, a chassis frame offset of 2126 mm, and a fork tine ground clearance of 225 mm, resulting in a bundle completion rate of 98.85% and a regular bale rate of 96.96%. Subsequent field tests with the optimized parameters showed that at a machine forward speed of 15.5 km/h, a chassis frame offset of 2126 mm, and a fork tine ground clearance of 225 mm, the bundle completion rate was 98.37% and the regular bale rate was 95.83%, meeting the relevant design requirements. This study can provide a reference for the design and development of straw collection and storage machinery.