Mobile relay (MR) selection is critical to the performance and realization of two-stage cooperative multicast (CM). Targeting at the energy efficiency and simplified realization, a location-aware distributed (LAD) MR selection method is proposed, where successful mobile stations (MSs) at the first stage that are farther from the base station would activate themselves to be MRs with higher probabilities. Assuming that the number of MRs close to an unsuccessful MS follows Poisson Point Process distribution, based on stochastic geometry, the coverage performance of two-stage CM with LAD MR selection can be numerically evaluated. Moreover, given the analytical results, an optimized LAD MR selection scheme can be designed, aiming at minimizing the total power consumption of two-stage CM. Numerical and simulation results verify that the analysis based on stochastic geometry is accurate. Overall, the optimized LAD MR scheme provides better energy efficiency and coverage performance than existing distributed MR schemes.