In this letter, a weighted minimum mean square error (WMMSE) empowered integrated sensing and communication (ISAC) system is investigated. One transmitting base station and one receiving wireless access point are considered to serve multiple users a sensing target. Based on the theory of mutual-information (MI), communication MI and sensing MI rate are utilized as the performance metrics under the presence of clutters. In particular, we propose an novel MI-based WMMSE-ISAC method by developing a unique transceiver design mechanism to maximize the weighted sensing and communication sum-rate of this system. Such a maximization process is achieved by utilizing the classical method -- WMMSE, aiming to better manage the effect of sensing clutters and the interference among users. Numerical results show the effectiveness of our proposed method, and the performance trade-off between sensing and communication is also validated.