Massive star formation occurs in giant molecular clouds (GMCs); an understanding of the evolution of GMCs is a prerequisite to develop theories of star formation and galaxy evolution. We report the highest-fidelity observations of the grand-design spiral galaxy M51 in carbon monoxide (CO) emission, revealing the evolution of GMCs vis-a-vis the large-scale galactic structure and dynamics. The most massive GMCs (giant molecular associations (GMAs)) are first assembled and then broken up as the gas flow through the spiral arms. The GMAs and their H2 molecules are not fully dissociated into atomic gas as predicted in stellar feedback scenarios, but are fragmented into smaller GMCs upon leaving the spiral arms. The remnants of GMAs are detected as the chains of GMCs that emerge from the spiral arms into interarm regions. The kinematic shear within the spiral arms is sufficient to unbind the GMAs against self-gravity. We conclude that the evolution of GMCs is driven by large-scale galactic dynamics-their coagulation into GMAs is due to spiral arm streaming motions upon entering the arms, followed by fragmentation due to shear as they leave the arms on the downstream side. In M51, the majority of the gas remains molecular from arm entry through the interarm region and into the next spiral arm passage.