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Under the impact of seismic forces, the strain of conventional anchor cables tended to increase sharply in an instant, which could easily cause the anchor cables to fail due to stress overload. This study aimed to optimize the design of rock supporting methods under dynamic disaster events such as earthquakes and rock bursts. A scale model specimen with a mechanical sliding device was designed based on an anti-seismic anchor cable. The working mechanism and seismic strain response of anti-seismic anchor cables were studied using static and shaking table model tests. The results show that under a static force, the anti-seismic anchor cables undergo in sequence a first elastic deformation stage, a slipping stage, a second elastic deformation stage, a plastic strengthening stage, and a brittle failure stage. In the slipping stage, the anchor cables start frictional sliding while keeping the axial force unchanged so as to adapt to the large deformation of the rock mass. The anti-seismic anchor cables exhibit the three situations of no-slip, instantaneous slip, and gradual and accumulative slip under seismic excitation. With a large constant resistance to slippage, the anchor cables do not slip, which can easily cause the anchor cables to break due to stress overload. With a small constant resistance to slippage, the reserved slipping distance is instantly exhausted; a step-shaped jump appears in the time history curves of the strain of the anchor cables. In the engineering design, a preset constant resistance to slippage is needed to match the seismic force for the anchor cables to exhibit the mechanism of multiple accumulated slips. During each slipping process, the strain of the anchor cables first decreases and then increases, with the peak strain decreasing significantly. This mechanism effectively cushions the instantaneous impact force of the earthquake, releases rock deformation, and dissipates seismic energy.