Abstract: Focused on complexity and confusion of factors influencing stability of loess slope of cut, this paper analyzed the calculation means of connective function and dependent degree in the appraise of slope of cut stability, and establish the classification criteria of slope of cut stability which is adapted to extension theory, combined with the topology engineering method and the stability assessment of loess slope of cut.The example evaluation consequence agrees with the result of fixed value calculation and project reality investigation.The assessment method of slope of cut stability based on extension theory presents a new feasible path for the problem which can settle stability assessment of the slope of cut.