Pruning is an essential agricultural practice for orchards. Proper pruning can promote healthier growth and optimize fruit production throughout the orchard's lifespan. Robot manipulators have been developed as an automated solution for this repetitive task, which typically requires seasonal labor with specialized skills. While previous research has primarily focused on the challenges of perception, the complexities of manipulation are often overlooked. These challenges involve planning and control in both joint and Cartesian spaces to guide the end-effector through intricate, obstructive branches. Our work addresses the behavior planning challenge for a robotic pruning system, which entails a multi-level planning problem in environments with complex collisions. In this paper, we formulate the planning problem for a high-dimensional robotic arm in a pruning scenario, investigate the system's intrinsic redundancies, and propose a comprehensive pruning workflow that integrates perception, modeling, and holistic planning. In our experiments, we demonstrate that more comprehensive planning methods can significantly enhance the performance of the robotic manipulator. Finally, we implement the proposed workflow on a real-world robot. As a result, this work complements previous efforts on robotic pruning and motivates future research and development in planning for pruning applications.