Mutation accumulation has been proposed as a cause of senescence. During this process, age-related genetic and epigenetic mutations steadily accumulate. Cascading deleterious effects of mutations might initiate a steady “accumulation of deficits” in cells, despite the existence of repair mechanisms, leading to cellular senescence and functional decline of tissues and organs, which ultimately manifest as frailty and disease. Here, we investigate several of these aspects in differentiating cell populations through modeling and simulation using the Moran birth–death (demographic) process, under several scenarios of mutation accumulation. Deleterious mutations seem to rapidly accumulate particularly early in the course of life, during which the rate of cell division is high, thereby exerting a greater effect on subsequent cellular senescence. Our results are compatible with the principle of the Muller’s ratchet taking place in asexually reproducing organisms. The ratchet speed in a given tissue depends on the size of the cell population, mutation rate and the impact of such mutations on cell phenotypes. It varies substantially among cells in different tissues and organs due to heterogeneity in relation to cell and organ-specific demographic features. Ratchet accelerates particularly after middle age, resulting in a synergistic fitness decay at the level of cell populations. We extend Fisher’s average excess concept and rank order scale to interpret differential phenotypic effects of the increase of the mutation load among cell populations within a given tissue. We postulate that classical evolutionary genetic models can explain, at least in part, the origins of frailty, subclinical conditions, morbidity and the health consequences of senescence.