This paper studies the effectiveness of relaying for interference mitigation in an interference-limited communication scenario. We are motivated by the observation that in a cellular network, a relay node placed at the cell edge observes a combination of intended signal and inter-cell interference that is correlated with the received signal at a nearby destination, so a relaying link can effectively allow the antennas at the relay and at the destination to be pooled together for both signal enhancement and interference mitigation. We model this scenario by a MIMO Gaussian relay channel with a digital relay-to-destination link of finite capacity, and with correlated noise across the relay and destination antennas. Assuming a compress-and-forward strategy with Gaussian input distribution and quantization noise, we propose a coordinate ascent algorithm for obtaining a stationary point of the non-convex joint optimization of the transmit and quantization covariance matrices. For fixed input distribution, the globally optimum quantization noise covariance matrix can be found in closed-form using a transformation of the relay's observation that simultaneously diagonalizes two conditional covariance matrices by congruence. For fixed quantization, the globally optimum transmit covariance matrix can be found via convex optimization. This paper further shows that such an optimized achievable rate is within a constant additive gap of the MIMO relay channel capacity. The optimal structure of the quantization noise covariance enables a characterization of the slope of the achievable rate as a function of the relay-to-destination link capacity. Moreover, this paper shows that the improvement in spatial degrees of freedom by MIMO relaying in the presence of noise correlation is related to the aforementioned slope via a connection to the deterministic relay channel.