It has been known that light possesses both spin and orbital angular momenta (AM) arising from the twisting behaviors of the electric (and magnetic) field vector and the wavefront of the field, respectively. The spin (AM) density is also a vector in the field of three dimensions (3D), since its orientation can be in any direction. In this Letter, we show that through focusing a Gaussian beam with both on-axis and off-axis vortices in a high-numerical-aperture system, the spin (AM) density vector in the focal region exhibits nontrivial behaviors: rotating around the central axis along the propagation direction. We demonstrate that this helical behavior of the spin (AM) density vector is mainly caused by the different Gouy phases of the three field components. By changing the position of the off-axis vortex and the semiaperture angle, the helical shape and the helical length can be adjusted. This is a new type of optical twist, to the best of our knowledge, and it may supply another rotational degree of freedom in optical tweezers.