Dormant pruning of fruit trees is an important task for maintaining tree health and ensuring high-quality fruit. Due to decreasing labor availability, pruning is a prime candidate for robotic automation. However, pruning also represents a uniquely difficult problem for robots, 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 paper, we introduce a system for pruning sweet cherry trees (in a planar tree architecture called an upright fruiting offshoot configuration) that integrates various subsystems from our previous work on perception and manipulation. The resulting system is capable of operating completely autonomously and requires minimal control of the environment. We validate the performance of our system through field trials in a sweet cherry orchard, ultimately achieving a cutting success rate of 58%. 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.