With the exhaustion of non-renewable resources and the increasing importance of essential materials for sustainable development, recycling is called into actions. For the critical mineral with positive minimum demand, this paper’s findings are threefold, regardless the market structure (social planner’s optimal choice or market competitions) and choice of strategy: (1) recycling technology can release partially the dependence on the supply of critical mineral, but the release only partially, given recycling depends on the accumulated supply before; (2) recycling technology postpones the pressure of the critical mineral’s exhaustion, but the postpone is as well not permanent; and (3) it is almost never an optimal strategy for the original resource players to hold back supply to the market.