The spatial variation of vector vortex beams with arbitrary polarization states and orbital angular momentum (OAM) values along the beam propagation is demonstrated by using plasmonic metasurfaces with the initial geometric phase profiles determined from the caustic theory. The vector vortex beam is produced by the superposition of deflected right- and left-handed circularly polarized component vortices with different helical phase charges, which are simultaneously generated off-axially by the single metasurface. Besides, the detailed evolution processes of intensity profile, polarization distribution and OAM value along the beam propagation distance is analyzed. The demonstrated arbitrary space-variant vector vortex beam will pave the way to many promising applications related to spin-to-orbital angular momentum conversion, spin-orbit hybrid entanglement, particle manipulation and transportation, and optical communication.