In practice, non-cooperative suspicious communications may be dynamic, that is, randomly in transmission or silence state, as a result, the traditional jamming mode may be inefficient or even ineffective. In this article, we design a sensing assisted integrated communication and jamming (SA-ICAJ) system, where the legitimate transceiver aims to communicate with multiple legitimate users while interfering with dynamic suspicious communications based on the results of spectrum sensing. Moreover, the rate splitting multiple access and artificial noise are both imbedded to alleviate the multi-user interference of legitimate communications and enhance jamming for suspicious communications, respectively. Further, we obtain a closed-form expression of optimal sensing time and propose a successive convex approximation based joint beamforming and rate optimization algorithm to maximize the sum average throughput of legitimate users while ensuring a certain jamming demand. Simulation results verify that the proposed scheme improves system performance compared with the baseline schemes.