We report on Q-switched waveguide lasers on the graphene-based crystalline Y-branch platform. By applying direct femtosecond laser writing of Nd:YAG laser crystal, a surface waveguide splitter with Y-branch geometry has been fabricated with depressed cladding configuration. The Q-switched lasing operation at 1064 nm is achieved in transmission mode, by attaching a two-layer graphene on the resonator output mirror, as well as by using interaction between the evanescent field and a few-layer graphene that was positioned right above the Y-type waveguide. Q-switched laser with a maximum average power of 173 mW, pulse energy and duration of 63 nJ and 90 ns is obtained. This work opens a way for laser-written crystalline devices as compact, direct-pump laser sources for diverse applications.