In this paper, we investigate the massive MIMO relay system, where the relay station (RS) forwards the signals from multiple remote users to the base station (BS). Large-scale antenna arrays in conjunction with low-resolution analog-to-digital converters (ADCs) are equipped at the RS and the BS to guarantee the high spectral efficiency with low cost. Considering the ever-present spatial correlation at both the RS and the BS, we first study the canonical channel estimation process, from which a tractable equivalent form of the channel estimate is extracted for further analysis. Under these transmission impairments along with the ADC quantization imperfection, we derive the closed-form approximation of the achievable rate. Then the impacts of power scaling, spatial correlation level, and ADC resolution bits are revealed comprehensively to guide the practical system deployment and implementation. Numerical results are presented to verify the theoretical analysis in a straightforward way.