Many small molecule chemotherapeutics induce stresses that globally inhibit mRNA translation, remodeling the cancer proteome and governing response to treatment. Here we measured protein synthesis in multiple myeloma cells treated with low-dose bortezomib by coupling pulsed-SILAC (pSILAC) with high-accuracy targeted quantitative proteomics. We found that direct measurement of protein synthesis by pSILAC correlated well with the indirect measurement of protein synthesis by ribosome profiling under conditions of robust translation. By developing a statistical model integrating longitudinal proteomic and mRNA-seq measurements, we found that proteomics could directly detect global alterations in translational rate as a function of therapy-induced stress after prolonged bortezomib exposure. Finally, the model we develop here, in combination with our experimental data including both protein synthesis and degradation, predicts changes in proteome remodeling under a variety of cellular perturbations. pSILAC therefore provides an important complement to ribosome profiling in directly measuring proteome dynamics under conditions of cellular stress.