Agriculture accounts for about one fifth of global greenhouse gas (GHG) emissions, making mitigation a key policy priority. Although policymakers are increasingly considering market-based approaches such as taxes, their broader impacts remain insufficiently assessed. This study examines the environmental, economic and social impacts of a GHG tax on Swiss agriculture. Using the agent-based sector model SWISSland, representing 3077 farms and capturing heterogeneous responses to taxation and structural change, we simulate tax levels of 100, 200 and 300 CHF/tCO2eq for 2024–2030. We consider three mitigation pathways: technical measures, structural changes in land use and livestock numbers, and farm exits. We assess their impacts on GHG emissions, nitrogen surpluses, biodiversity, farm income, food production and food security. A GHG tax activates abatement mechanisms and induces dairy herd reductions, grassland extensification, shifts towards crop production for direct human consumption, and livestock farm exits. At 100 and 200 CHF/tCO2eq, emission reductions are mainly driven by technical measures, whereas at 300 CHF/tCO2eq they increasingly result from structural adjustment, including livestock farm exits and land reallocation to less emissions-intensive production. A tax of 100 CHF/tCO2eq reduces emissions by 5%, while higher tax rates achieve greater reductions but increase sectoral income losses from 13% to 25%. Food self-sufficiency and calorie production remain stable. The model also shows environmental co-benefits, including lower nitrogen surpluses and increased biodiversity areas. These findings highlight synergies and trade-offs across sustainability dimensions and suggest that redistributing tax revenues could mitigate adverse effects and improve policy outcomes, while enhancing the policy's social acceptability.