Tropical dry woodlands and savannas harbour high levels of biodiversity and carbon, but are also important regions for agricultural production. This generates trade-offs between agriculture and the environment, as agricultural expansion and intensification typically involve the removal of natural woody vegetation. Cattle ranching is an expanding land use in many of these regions, but how different forms of ranching mediate the production/environment trade-off remains weakly understood. Here, we focus on the Argentine Chaco, to evaluate trade-offs between beef production and carbon storage in grazing systems with different levels of woody cover (n = 27). We measured beef productivity and carbon storage during 2018/19 and used a regression framework to quantify the trade-off between both, and to analyze which agroclimatic and management variables explain the observed trade-off. Our main finding was that silvopastures had the lowest trade-off between beef production and carbon storage, as management in these systems seeks to increase herbaceous forage by removing shrubs, while maintaining most of the bigger trees that contain most above-ground carbon. The most important variable explaining the beef production/carbon storage trade-off was pasture management, specifically the number of shrub encroachment control interventions, with a lower trade-off for higher numbers of interventions. Unfortunately, more interventions can also result in woody cover degradation over time, and shrub encroachment management must therefore be improved to become sustainable. Overall, our study highlights the strong environmental trade-offs associated with beef production in dry woodlands and savanna, but also the key role of good management practices in lowering this trade-off. Specifically, silvopastoral systems can increase beef production as much as converting woodlands to tree-less pastures, but silvopastures retain much more carbon in aboveground vegetation. Silvopastoral systems thus represent a promising land-use option to lower production/environment trade-offs in the Dry Chaco and likely many other tropical dry woodlands and savanna.