In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.