We report on the first Tm-doped double tungstate microchip laser Q-switched with graphene using a Tm:KLu(WO4)2 crystal cut along the Ng dielectric axis. This laser generates a maximum average output power of 310 mW with a slope efficiency of 13%. At a repetition rate of 190 kHz the shortest pulses with 285 ns duration and 1.6 μJ energy are achieved.