A watt-level passively Q-switched ytterbium-doped double-cladding fiber laser with a graphene oxide (GO) absorber was demonstrated. The structure of the GO saturable absorber mirror (GO-SAM) was of the sandwich type. A maximum output power of 1.8 W was obtained around a wavelength of 1044 nm. To the best of our knowledge, this is the highest output power in Q-switched fiber lasers based on a GO saturable absorber. The pure GO was protected from the oxygen in the air so that the damage threshold of the GO-SAM was effectively raised. The gain fiber was a D-shaped ytterbium-doped double-cladding fiber. The pulse repetition rates were tuned from 120 to 215 kHz with pump powers from 3.89 to 7.8 W. The maximum pulse energy was 8.37 μJ at a pulse width of 1.7 μs.