In order to improve the performance of slip and reduce the extrusion damage of the drill pipe in the drill rig, the optimization of structural parameters and teeth shape of the slip while clamping the drill pipe had been researched in this article. On the macroscale, the structural parameters of the slip had been optimized with response surface method (RSM) and Multiobjective Genetic Algorithm (MOGA). The optimized result showed that the single weight of the slip had been reduced from 3.99 kg to 2.91 kg and the maximum deformation of the drill pipe was reduced from 3.75 mm on both sides to 2.56 mm on both sides. On the microscale, a mathematical model for the single slip teeth while clamping the drill pipe had been established to give a detailed description to calculate the equivalent coefficient of friction and provide the relationship between the frictional torque with the allowable compression strength. In addition, the finite element model that had been set up by ABAQUS was used to verify the mathematical model, and the comparison of results had shown the accuracy of the mathematical model of the slip teeth while clamping the drill pipe. According to the mathematical model of the slip teeth in the drill rig, while clamping the drill pipe, the optimal shape of the slip teeth in the drill rig was achieved under the following condition: the slope of the slip teeth θ is 60°, the top width of the slip teeth
w
h
is 1.5 mm, and the depth of the slip teeth clamping the drill pipe d is 0.5 mm. The equivalent coefficient of friction
f
v
can be increased from 1.73 to 2.06, and the optimal result
f
v
increases 11.3%.