Human actions led to the worldwide decline of marine mammal populations in the 18th-19th centuries. However, the global uptake in protective legislation during the 20th century has recently allowed many marine mammal populations to recover. This positive trend is particularly true of pinnipeds (e.g., seals and sea lions), whose recovering populations are increasingly in conflict with fisheries. Many fisheries organisations call for managed culls of sea lion populations to reduce competition for target fish species as well as damage to catch and fishing gear through operational interactions. However, despite widespread perceptions that sea lion populations are generally increasing, to-date culls have been considered or implemented without quantitative evidence of their impacts on seal lion population viability. This knowledge gap is particularly concerning given the expected increase in extreme climate conditions, such as extreme El Niño events, which together with culls could push sea lion populations in some parts of the world into the extinction vortex. In this analysis, I develop and parameterise stochastic matrix population models of the South American sea lion (Otaria flavescens) to project the impact of (1) three cull scenarios with different intensity and temporal frequency targeting adult females, (2) extreme El Niño events whose frequency is modelled using a Markovian transition matrix, (3) and the interaction of culls and extreme climate events on population dynamics. I focus on the Chilean population of O. flavescens, where recent increases in sea lion numbers have triggered widespread conflict with small-scale fisheries, and where sea lion populations will increasingly be affected by extreme El Niño conditions. I find that sea lion populations decline below minimum viable population sizes under all scenarios involving culls and extreme climate events. By explicitly considering parameter uncertainty, this approach is a call to action for future research to focus on collecting stage-specific, annual population data to reduce uncertainty regarding marine mammal vital rates.