Trees are long-lived plants that develop highly branched shoot systems over time. During growth, somatic mutations accumulate along these branching structures and can become fixed in reproductive tissues such as flowers and fruits. Because mature trees produce tens of thousands of terminal branches, each harboring potentially mutated gametes, limiting the accumulation of somatic mutations is critical to avoid mutational meltdown and inbreeding depression. Although recent evidence suggests that long-lived plants have evolved mechanisms to suppress mutation accumulation, the developmental basis for this remains unclear. Here we develop a theoretical model that connects crown development with cell lineage sampling to show that branching architecture can strongly suppress somatic mutation accumulation in trees, often to the same extent as reducing the mutation rate itself. Specifically, tree forms that promote developmental path-sharing among branches suppress the number of unique mutational lineages in the crown. We find that this architectural effect can alter mutation burden by orders of magnitude, even when mutation rates and terminal branch numbers remain constant. These insights suggest that branching strategies may evolve not only to optimize growth and resource allocation, but also to limit the accumulation of somatic variants during ontogeny.