Wireless information surveillance, by which suspicious wireless communications are closely monitored by legitimate agencies, is an integral part of national security. To enhance the information surveillance capability, we propose in this paper a new proactive eavesdropping approach via a spoofing relay, where the legitimate monitor operates in a full-duplex manner with simultaneous eavesdropping and spoofing relaying to vary the source transmission rate in favor of the eavesdropping performance. To this end, a power splitting receiver is proposed, where the signal received at each antenna of the legitimate monitor is split into two parts for information eavesdropping and spoofing relaying, respectively. We formulate an optimization problem to maximize the achievable eavesdropping rate by jointly optimizing the power splitting ratios and relay beamforming matrix at the multi-antenna monitor. Depending on the suspicious and eavesdropping channel conditions, the optimal solution corresponds to three possible spoofing relay strategies, namely \emph{constructive relaying}, \emph{jamming}, and \emph{simultaneous jamming and destructive relaying}. Numerical results show that the proposed technique significantly improves the eavesdropping rate of the legitimate monitor as compared to the existing passive eavesdropping and jamming-based eavesdropping schemes.