The modular multilevel converter (MMC) is widely used in flexible direct current projects. The fault clearance speed of hybrid MMCs is closely related to the proportion of full bridge sub-modules (FBSMs). To address the issue of sub-module overvoltage caused by unbalanced energy absorption between half bridge sub-modules (HBSMs) and FBSMs during the clearance of a bipolar short-circuit fault, this paper designs an energy-assisted isolation branch suitable for hybrid MMCs with a low FBSM ratio. By bypassing the HBSMs before blocking, the energy released by the submodules is reduced, thereby lessening the transient energy absorption burden on the FBSMs and suppressing FBSM overvoltage. To shorten the fault clearance time, this paper proposes a dual-branch coordinated operation strategy. A transient energy absorption branch is connected in parallel at the port side to assist in absorbing the fault's transient energy and accelerate fault clearance. A two-terminal hybrid MMC-based flexible direct current transmission system model is built on the PSCAD/EMTDC platform to verify the effectiveness of the proposed scheme. Simulation results show that the proposed dual-branch coordinated operation strategy can effectively suppress sub-module overvoltage, shorten the fault clearance time, and reduce the operational cost associated with rapid self-clearing of faults in hybrid MMCs.