We experimentally demonstrated a wavelength switchable passively mode-locked Yb:LuAG laser. The mode locked laser wavelength could be switched between 1031 nm and 1046 nm by a slit. With a coupler of 2% transmission, mode locked pulses with pulse duration of 1.15 ps and average output power of 1.3 W were generated at 1031 nm. By simply translating the slit position, 1046-nm mode locked pulses were generated with pulse duration of 252 fs and average output power of 676 mW. With the output coupler of 8% transmission, higher average output power of 2.2 W was generated at 1031 nm with pulse duration of 1.8 ps, which is the highest average output power ever reported for Yb:LuAG mode-locked lasers.