The loop-free single-layer hyperbolic cable net structure (LSHCS) is a new tensile cable structure for buildings, and it can overcome the disadvantages of key elements and the high tension in tensile cable structures with loop cables. The imperfection of the LSHCS is that cable clamps near the inside boundary are redundant. In this paper, the static behavior and dynamic characteristics of thirty-one schemes in five levels of deleting cable clamps are carried out with ANSYS software and Midas/Gen software. The results show that SE1/1, SE2/1, SE3/1, and SE4/1 are the best cable clamp deleting schemes for their respective levels. Displacements are the most sensitive to deleting cable clamps, the natural vibration period comes in second, and tensions are not sensitive with the growth rates of 6.09%, 5.11%, 15.97%, and 19.28% in the best scheme of each level. It is concluded that schemes involving the virtual rings of cable clamps closest to the inside boundary cause the smallest effect on static behavior and dynamic characteristics. Deleting the cable clamps affects the structural stiffness significantly, but the bearing capacity is not seriously affected. It turns out that removing redundant cable clamps in the dense part of the LSHCS is feasible.