The accumulation of magmatic CO₂ beneath low-permeability barriers may lead to the formation of CO₂-rich gas reservoirs within volcanic systems. Such accumulation is often evidenced by high surface CO₂ emissions that fluctuate over time. The temporal variability in surface degassing is believed in part to reflect a complex interplay between deep magmatic degassing and the permeability of degassing pathways. A better understanding of the dynamics of CO₂ degassing is required to improve monitoring and hazards mitigation in these systems. Owing to the availability of long-term records of CO₂ emissions rates and seismicity, Mammoth Mountain in California constitutes an ideal site towards such predictive understanding. Mammoth Mountain is characterized by intense soil CO₂ degassing (up to ∼1000 t d⁻¹) and tree kill areas that resulted from leakage of CO₂ from a CO₂-rich gas reservoir located in the upper ∼4 km. The release of CO₂-rich fluids from deeper basaltic intrusions towards the reservoir induces seismicity and potentially reactivates faults connecting the reservoir to the surface. While this conceptual model is well-accepted, there is still a debate whether temporally variable surface CO₂ fluxes directly reflect degassing of intrusions or variations in fault permeability. Here, we report the first large-scale numerical model of fluid and heat transport for Mammoth Mountain. We discuss processes (i) leading to the initial formation of the CO₂-rich gas reservoir prior to the occurrence of high surface CO₂ degassing rates and (ii) controlling current CO₂ degassing at the surface. Although the modeling settings are site-specific, the key mechanisms discussed in this study are likely at play at other volcanic systems hosting CO₂-rich gas reservoirs. In particular, our model results illustrate the role of convection in stripping a CO₂-rich gas phase from a rising hydrothermal fluid and leading to an accumulation of a large mass of CO₂ (∼10⁷–10⁸ t) in a shallow gas reservoir. Moreover, we show that both, short-lived (months to years) and long-lived (hundreds of years) events of magmatic fluid injection can lead to critical pressures within the reservoir and potentially trigger fault reactivation. Our sensitivity analysis suggests that observed temporal fluctuations in surface degassing are only indirectly controlled by variations in magmatic degassing and are mainly the result of temporally variable fault permeability. Finally, we suggest that long-term CO₂ emission monitoring, seismic tomography and coupled thermal–hydraulic–mechanical modeling are important for CO₂-related hazard mitigation.