Human-caused mortality of wildlife is a pervasive threat to biodiversity. Assessing the population-level impact of fisheries bycatch and other human-caused mortality of wildlife has typically relied upon deterministic methods. However, population declines are often accelerated by stochastic factors that are not accounted for in such conventional methods. Building upon the widely applied Potential Biological Removal (PBR) equation, we introduce a new population modeling approach for estimating sustainable limits to human-caused mortality, and applied this to a case study of bottlenose dolphins impacted by capture in an Australian demersal otter trawl fishery. Our approach, termed ‘Sustainable Anthropogenic Mortality in Stochastic Environments’ (SAMSE), incorporates environmental and demographic stochasticity, including the dependency of offspring on their mothers. The SAMSE-limit indicates the maximum number of individuals that can be removed without causing negative stochastic population growth. We calculated a PBR of 16.2 dolphins per year using the best abundance estimate available. In contrast, the SAMSE model indicated that only 2.3 to 8.0 dolphins could be removed annually without causing a population decline in a stochastic environment. The results suggest that reported bycatch rates are unsustainable in the long-term, unless reproductive rates were consistently higher than average. The difference between the deterministic PBR calculation and SAMSE mortality limits illustrates that deterministic approaches may underestimate the true impact of human-caused mortality of wildlife. This highlights the importance of integrating stochasticity when evaluating the impact of bycatch or other human-caused mortality on wildlife, such as hunting, lethal control measures or wind turbine collisions. Although population viability analysis (PVA) has previously been used to evaluate the impact of human-caused mortality, SAMSE represents a novel methodological PVA framework that incorporates stochasticity for estimating acceptable levels of human-caused mortality. It offers a broadly applicable, stochastic addition to the demographic toolbox to evaluate the impact of human-caused mortality on wildlife.