The evolution of the spin density vectors (SDVs) is studied in a strongly focused composite field. It is found that the SDVs can be spiral along the propagation axis, and they are perpendicular to the $y_s$ direction on the $y_s$ axis. This behavior is governed by the Gouy phase difference between the field polarization components. The $60°$ rotation of the spatial distribution of the transverse SDVs is also generated, which is found to be controlled by the Gouy phase difference between the field orbital angular momentum modes. Additionally, the spin density singularities are observed in the evolution of the SDVs.