Our understanding of ocean mixing is challenged by its patchy, episodic nature and a scarcity of direct measurements, especially in the Arctic Ocean. In this study, we exploit a historical record of nearly 3,000 conductivity‐temperature‐depth profiles collected in the shelf and shelf‐slope waters of the Canadian Arctic Ocean from 2002 to 2016 to characterize the variability of 28,872 internal wave‐driven turbulent dissipation and mixing rate estimates from a finescale parameterization. We find that these estimates of wave‐driven dissipation rates and associated diapycnal diffusivities are generally low, but exhibit wide variability, each spanning several orders of magnitude. We further find that stratification plays a significant role in modulating the mixing rate both vertically and regionally within the study domain. Dissipation rate and diffusivity estimates display a weak seasonal cycle, but no evidence of statistically significant interannual trends over this period. Exceptionally large localized temporal variability appears to dominate other potential underlying patterns. The presence of strong upper ocean stratification combined with predominately weak dissipation rate estimates implies that many regions in the Canadian Arctic Ocean are likely in a molecular or buoyancy‐controlled mixing regime. Even when the concept of a turbulent‐enhanced diffusivity is potentially relevant, most turbulent heat flux estimates out of the Atlantic Water thermocline are smaller than the average value required to close the standardly assumed Arctic Ocean heat budget. In contrast, we find evidence for isolated occurrences of anomalously large heat fluxes, which may disproportionately contribute to the liberation of Atlantic Water heat toward the surface sea ice pack.