Agricultural activity has been identified as a considerable source of Greenhouse Gas (GHG) emissions. Emissions from ruminant livestock farms are produced particularly due to CH4 emissions from enteric fermentation. Dairy sheep farming is the most important livestock production activity in Greece, characterized by a high degree of farm diversification. This paper addresses the issue of the evaluation of GHG emissions of Greek dairy sheep farms, through the use of a whole farm mathematical programming model that uses farm level data and optimizes total gross margin. Mathematical programming models are an appropriate tool, when addressing complex issues, such as GHG emissions. The analysis is undertaken on different farm types, instead of a representative farm, to account for the heterogeneity of the sheep farming activity. Thus, marginal abatement cost and appropriate mitigation strategies for diversified farms are determined. The results indicate that intensive farms cause few emissions per produced milk (2.7kg of CO2 eq). Also, the marginal abatement cost ranges among 51-64€/t for all types of sheep farms (at 20% abatement level). The model used in this analysis and the results it yields are useful to researchers and policy makers, who aim to design efficient mitigation measures.