Large topological charge optical vortex beams carrying orbital angular momentum have potential applications on optical trapping, optical communication with high capacity, quantum information processing. However, the beam quality is degraded in vortex beams generated with spiral phase plates or resonator mirrors with defect spots and optical conversion efficiency in solid-state lasers is sacrificed by controlling the loss of resonator. It is a big challenge for generating high beam quality, high-order cylindrical vector beams with large topological charge in compact solid-state lasers. Here, high-order cylindrical vector beams [Laguerre-Gaussian (LG) modes with zero degree and order of l, LG0,l] with tunable topological charges up to 14 have been generated in an annular beam pumped Yb:YAG microchip laser by manipulating the pump power-dependent population inversion distribution. Efficient performance with optical efficiency of 17.5% has been achieved. The output power is 1.36 W for a vector-vortex laser with 14 topological charges. The pump power dependent wavelength tunable and dual-wavelength laser oscillation in vector-vortex beams has been observed by controlling the reabsorption loss at 1030 nm. Wavelength tunable, dual-wavelength (1030 and 1050 nm) laser oscillation has been achieved for vector-vortex beams with topological charges of 8, 9, and 10. The laser beam quality factor M2 close to the theoretical value (l + 1) has been achieved for LG0,l vector-vortex beams with tunable topological charges up to 14. This work provides a new effective method for generating large topological charge high-order cylindrical vector beams in solid-state microchip lasers with high efficiency and high beam quality.