Proliferating animal cells maintain a stable size distribution over generations despite fluctuations in cell growth and division size. Previously, we showed that cell size control involves both cell size checkpoints, which delay cell cycle progression in small cells, and size-dependent regulation of mass accumulation rates (Ginzberg et al., 2018). While we previously identified the p38 MAPK pathway as a key regulator of the mammalian cell size checkpoint (Liu et al., 2018), the mechanism of size-dependent growth rate regulation has remained elusive. Here, we quantified global rates of protein synthesis and degradation in cells of varying sizes, both under unperturbed conditions and in response to perturbations that trigger size-dependent compensatory growth slowdown. We found that protein synthesis rates scale proportionally with cell size across cell cycle stages and experimental conditions. In contrast, oversized cells that undergo compensatory growth slowdown exhibit a superlinear increase in proteasome-mediated protein degradation, with accelerated protein turnover per unit mass, suggesting activation of the proteasomal degradation pathway. Both nascent and long-lived proteins contribute to the elevated protein degradation during compensatory growth slowdown, with long-lived proteins playing a crucial role at the G1/S transition. Notably, large G1/S cells exhibit particularly high efficiency in protein degradation, surpassing that of similarly sized or larger cells in S and G2, coinciding with the timing of the most stringent size control in animal cells. These results collectively suggest that oversized cells reduce their growth efficiency by activating global proteasome-mediated protein degradation to promote cell size homeostasis.