With the popularity of low-carbon economy, governments of all countries have introduced energy-saving and emission reduction policies. Crowdsourcing logistics, a logistics assignment model developed under the sharing economy, can effectively use transport resources from the public and thus meaningfully contribute to sustainability. It has important practical significance both for energy saving and emission reduction in last-mile logistics distributions, and hence plays an important role in tackling the challenges associated with last-mile and same-day deliveries. This paper investigated the crowdsourcing logistics task assignment problem where logistics platforms can perform multi-stage task assignment. The information of all tasks to be delivered in each stage is known a priori, however the information of crowdsourcing drivers in future stages is not known completely. A multi-stage two-echelon dynamic task assignment model (MS-2E-DAM) was developed for the problem and a heuristic which combines genetic algorithm and tabu search (GA-TS) was developed. Its performance was benchmarked with CPLEX 12.10 for small-size problems and the results demonstrated the effectiveness of the proposed heuristic approach. For large-size problems, the proposed approach can help reduce the overall cost by 1.94% over traditional assignment approaches. Sensitivity analyses on three key parameters helped identify the key factors that affect the system cost, and several management suggestions were proposed based on the results.