A dual-off-axis pumping scheme is presented to generate wavelength-tunable high-order Hermite-Gaussian (HG) modes in Yb:CaGdAlO4 lasers. The mode and wavelength can be actively controlled by the off-axis displacements and pump power. The purities of the output HG modes are quantified by intensity distributions and the measured M2 values. The highest order reaches m=15 for stable HGm,0 mode, and wavelength-tunable width is about 10 nm. Moreover, through externally converting the HGm,0 modes, the vortex beams carrying orbital angular momentum (OAM) with a large OAM-tunable range from ±1ℏ to ±15ℏ are produced. This work is effective for largely scaling the spectral and OAM tunable ranges of optical vortex beams.