Surface acoustic wave (SAW) radio-frequency identification (RFID) has high potential for industrial applications, where automated identification and localization of assets represent the backbone of process controlling and logistics. However, in situations where multiple tags are simultaneously interrogated, the response patterns corresponding to the hard-coded reflectors are prone to overlap, preventing their association with the corresponding tags and, hence, the correct tag decoding. Identification and localization of multiple SAW RFID tags are addressed in this work under this challenging effect, known as collision, with a multi-antenna mobile robot-based synthetic aperture approach. Using the estimation of the spatial probability density functions of the SAW tag reflectors over a given interrogation aperture, the received impulse responses can be resolved in three dimensions and clustered with respect to their estimated locations. The performance of the proposed approach to associate and localize the signals from multiple tags was evaluated theoretically and experimentally.