In a coupled-cavity system consisting of a single-cavity optomechanical system and an auxiliary cavity, we theoretically investigate the characteristics of optomechanically induced amplification and the slow light effect. The results show that if we adopt a high-quality auxiliary cavity (with a small decay rate), the strength of the probe field in the system can be strongly amplified. Based on the perfect optomechanically induced transparency, we also find that the time delay in this model can easily surpass its upper bound in the single-cavity optomechanical system. Additionally, the system is used to study the interesting phenomenon of perfect optomechanically induced absorption. We believe that the results can be used to control optical transmission in modern optical networks.