Development of an accurate and automated algorithm to completely segment cervical cells in Pap images is still one of the most challenging tasks. The main reasons are the presence of overlapping cells and the lack of guiding mechanism for the convergence of ill-defined contours to the actual cytoplasm boundaries. In this paper, we propose a novel method to address these problems based on level set method (LSM). Firstly, we proposed a morphological scaling-based topology filter (MSTF) and derived a new mathematical toolbox about vector calculus for evolution of level set function (LSF). Secondly, we combine MSTF and the mathematical toolbox into a multifunctional filtering algorithm 2D codimension two-object level set method (DCTLSM) to split touching cells. The DCTLSM can morphologically scale up and down the contour while keeping part of the contour points fixed. Thirdly, we design a contour scanning strategy as the evolution method of LSF to segment overlapping cells. In this strategy, a cutting line can be detected by morphologically scaling the union LSF of the pairs of cells. Then, we used this cutting line to construct a velocity field with an effective guiding mechanism for attracting and repelling LSF. The performance of the proposed algorithm was evaluated quantitatively and qualitatively on the ISBI-2014 dataset. The experimental results demonstrated that the proposed method is capable of fully segmenting cervical cells with superior segmentation accuracy compared with recent peer works.