Shared autonomous electric vehicles (SAEVs) can offer safer, more efficient, and more environmentally friendly real-time mobility services with advanced autonomous driving technologies. In this study, a multi-agent-based simulation model considering SAEVs’ vehicle range and charging behavior is proposed. Based on real-world datasets from the Luohu District in Shenzhen, China, various scenarios with different fleet sizes, charging rates, and vehicle ranges are established to evaluate the impact of these parameters on parking demand, charging demand, vehicle miles traveled (VMT), and response time in the era of SAEVs. The results show there would be much more charging demand than parking demand. Moreover, a larger fleet size and longer vehicle range would lead to more parking demand, more charging demand, and more VMT while increasing the charging rate can dramatically reduce the charging demand and VMT. Average response time can be reduced by increasing the fleet size or the charging rate, and a larger vehicle range leads to longer response time due to the longer time spent recharging. It is worth noting that the VMT generated from relocating from the previous request destination to the origin of the upcoming request accounts for nearly 90% of the total VMT, which should be addressed properly with appropriate scheduling. A charging policy considering current requests and the availability of charging stations was proposed and verified in terms of reducing the response time by 2.5% to 18.9%.