Recently, the concept of green development is attracted intensively with the continuous improvement of the requirements of ecological civilization construction in the new era. Simultaneously, the discharge and pollution of waste from university laboratories are greatly attracting attention from all sectors of society. Based on the current situation of waste disposal in university laboratories, the evolutionary game model between laboratories and third-party recyclers is constructed and the disposal strategy choices and evolutionary trends of both sides in the case of perfect competition or cooperation are analyzed. Those results indicate that cooperation is the best choice for them to increase profits, albeit laboratories and third parties may change their cooperation and competitive strategies over time. Moreover, the optimal reward and punishment mechanism is conducive to promoting their cooperation trend and boosting their profits.