We devise a stochastic and spatially explicit model for the dynamics of the initials cells in a stratified shoot apical meristem (SAM). The meristem is composed of three layers with seven initials per layer. We investigate the probability and number of divisions for a mutant lineage to either reach fixation or becoming purged through selection or drift. In contrast to previous studies our results show that the functional organization of the initials in stratified SAMs acts as an efficient purging mechanism particularly of deleterious mutations. All mutants are rapidly purged when deleterious. The probability of fixation for mutants with a higher fitness than the wild type increases linearly up to 70%. The median number of divisions to fixation of both genotypes is insensitive to the mutant's fitness. The median number of divisions to wild-type fixation is less than 100, with the upper quartile below 200. The largest number of divisions to wild-type fixation are in the order of 100 000 divisions. Our results indicate that the spatial organization of SAM enables the efficient purging of mutant lineages, particularly if they are deleterious. On the other hand, long-lived chimeric stages are common when mutant lineages succeed to overcome the initial numerical disadvantage.