The double Debye model has been used to understand the dielectric response of different types of biological tissues at terahertz (THz) frequencies but fails in accurately simulating human breast tissue. This leads to limited knowledge about the structure, dynamics, and macroscopic behavior of breast tissue, and hence, constrains the potential of THz imaging in breast cancer detection. The first goal of this paper is to propose a new dielectric model capable of mimicking the spectra of human breast tissue's complex permittivity in THz regime. Namely, a non-Debye relaxation model is combined with a single Debye model to produce a mixture model of human breast tissue. A sampling gradient algorithm of nonsmooth optimization is applied to locate the optimal fitting solution. Samples of healthy breast tissue and breast tumor are used in the simulation to evaluate the effectiveness of the proposed model. Our simulation demonstrates exceptional fitting quality in all cases. The second goal is to confirm the potential of using the parameters of the proposed dielectric model to distinguish breast tumor from healthy breast tissue, especially fibrous tissue. Statistical measures are employed to analyze the discrimination capability of the model parameters while support vector machines are applied to assess the possibility of using the combinations of these parameters for higher classification accuracy. The obtained analysis confirms the classification potential of these features.