Dormant pruning is an important orchard activity for maintaining tree health and producing high-quality fruit. Due to decreasing worker availability, pruning is a prime candidate for robotics. However, pruning also represents a uniquely difficult problem, requiring robust systems for perception, pruning point determination, and manipulation that must operate under variable lighting conditions and in complex, highly unstructured environments. In this article, we introduce a system for pruning modern planar orchard architectures with simple pruning rules that combines various subsystems from our previous work on perception and manipulation. The integrated system demonstrates the ability to autonomously detect and cut pruning targets with minimal control of the environment, laying the groundwork for a fully autonomous system in the future. We validate the performance of our system through field trials in a sweet cherry orchard, ultimately achieving a cutting success rate of 58% across 10 trees. Though not fully robust and requiring improvements in throughput, our system is the first to operate on fruit trees and represents a useful base platform to be improved in the future.