Searchable encryption (SE) is one of the key enablers for building encrypted databases. It allows a cloud server to search over encrypted data without decryption. Dynamic SE additionally includes data addition and deletion operations to enrich the functions of encrypted databases. Recent attacks exploiting the leakage in dynamic operations drive rapid development of new SE schemes revealing less information while performing updates; they are also known as forward and backward private SE. Newly added data is no longer linkable to queries issued before, and deleted data is no longer searchable in queries issued later. However, those advanced SE schemes reduce the efficiency of SE, especially in the communication cost between the client and server. In this paper, we resort to the hardware-assisted solution, aka Intel SGX, to ease the above bottleneck. Our key idea is to leverage SGX to take over the most tasks of the client, i.e., tracking keyword states along with data addition and caching deleted data. However, handling large datasets is non-trivial due to the I/O and memory constraints of the SGX enclave. We further develop batch data processing and state compression technique to reduce the communication overhead between the SGX and untrusted server, and minimise the memory footprint in the enclave. We conduct a comprehensive set of evaluations on both synthetic and real-world datasets, which confirm that our designs outperform the prior art.