In this paper, the geometric structures and the melting-like processes of the 13-atom pure copper, pure cobalt cluster and their 13-atom mixed clusters are investigated and compared by the molecular dynamics method. The calculation shows that the pure copper and cobalt clusters have the standard icosahedral structures and the mixed clusters take on the deformed icosahedral structures. The quantitative analysis shows that the deformations are slight. Moreover, an element similarity function is introduced by which the contribution of the compositions of the clusters to the deformation of the mixed clusters is analyzed and discussed. With the increase of the temperature, the migrating and recombination of the atoms on the surface of the clusters are observed, indicating the starting of the transition from solid-like to liquid-like state for the clusters. Through the calculating of the relative root-mean-squared pair separation fluctuation and monitoring the dynamical structures of the clusters, it is found that the mixed clusters experience a multi-step process in the transition.