Trees accumulate somatic mutations throughout their long lifespan, resulting in genetic mosaicism among branches. Recent advances in sequencing technology have enabled quantitative identification of these mutations. In this study, we developed mathematical models to estimate the dynamic process of somatic mutation accumulation from snapshot genomic data obtained from long-lived tropical trees of the Dipterocarpaceae family, which dominate tropical rainforests in Southeast Asia. Our models focus on genetic differences between shoot apical meristems (SAMs) at branch tips and explicitly incorporate stem cell dynamics within SAMs during shoot elongation and branching, enabling to quantify somatic genetic drift arising from stem cell lineage replacement. By comparing model predictions with empirical data from Dipterocarpaceae trees, we estimated parameters governing stem cell dynamics and somatic mutation rates. Our results indicate that both shoot elongation and branching involve replacement of stem cell lineages, leading to a moderate degree of somatic genetic drift. When stem cell dynamics were considered, the inferred mutation rates were slightly lower than previous estimates that ignored these processes. Using the estimated parameters, we further performed stochastic simulations to predict patterns of somatic mutations, including patterns not directly observed in the sampled trees, such as occasional deviations of somatic mutation phylogenies from physical architecture. Together, our modeling framework provides insights into how genetic mosaicism is structured within long-lived tropical trees and reveals the stem cell dynamics underlying their long-term growth and accumulation of somatic mutations.