In real applications, it is very common to have the true clustering structure masked by the presence of noise variables and/or dimensions. A mixture model is proposed for simultaneous clustering and dimensionality reduction of mixed-type data: the continuous and the ordinal variables are assumed to follow a Gaussian mixture model, where, as regards the ordinal variables, it is only partially observed. To recognize discriminative and noise dimensions, the variables are considered to be linear combinations of two independent sets of latent factors where only one contains the information about the cluster structure while the other one contains noise dimensions. In order to overcome computational issues, the parameter estimation is carried out through an EM-like algorithm maximizing a composite log-likelihood based on low-dimensional margins.