In mining engineering, coal and gas outburst is extremely dangerous dynamic disaster, which will cause serious casualties and property losses. As a method to predict coal burst, the drilling cutting method has been widely used in coal mines. The drilling cutting weight is an important index of the drilling cutting method. In theoretical calculation, scholars usually assume that the coal is isotropic and homogeneous before drilling to deduce the formula of drilling cutting weight. However, in actual mining engineering, drilling cutting is usually carried out in the plastic coal body in front of the working face. Therefore, in the present study, the theoretical formula of the drilling cutting weight in the plastic coal mass is deduced, as well as in the elastic coal mass. The results show that the drilling cutting weight calculated based on the deduced formula increases with the increase of drilling depth in the plastic coal mass, which is consistent with the field measurement results. The fragmentation degrees of coal around the drilling hole are also considered by introducing cohesion, which changes linearly along the radial direction of the drilling hole. The results show that the smaller the cohesion, the greater the drilling cutting weight. The calculation formula for drilling cutting in elastic coal mass is also given. The dilatancy effect of coal around the drilling hole is also considered by introducing expansion coefficient n, which changes linearly along the radial direction of the drilling hole. There is a good match between the theoretical calculation results and the laboratory test results. The obtained results are helpful for the prediction and prevention of coal burst.