The installation of Phasor Measurement Units (PMUs) is a step towards achieving wide-area situational awareness for the power grid. PMUs utilize GPS signals for time synchronization and are vulnerable to GPS Spoofing Attacks (GSAs) as civilian GPS signals are unencrypted and have low signal power. We propose a novel Residual-based Spoofing Detection and Measurement Correction (RSDMC) algorithm for the power grid that detects GSAs and corrects spoofed PMU measurements. During one or multiple GSAs, RSDMC iteratively minimizes the residual norm to correct spoofed PMU measurements. We derive a necessary condition for our proposed algorithm to show that the residual norm increases during GSAs. We perform Monte Carlo simulations to verify our derived necessary condition. We further simulate the IEEE 14, IEEE 118, and Illinois 200 bus test cases to validate RSDMC against multiple GSAs.