This paper studies the influence of geometric structure cutting on transverse crack treatment with the discrete elements method (DEM). Suitable strategies for geometrical structure cutting are put forward. The two-dimensional DEM model of asphalt mixture was established firstly. The asphalt mixture was simplified into a combination of voids, coarse aggregates, and asphalt mortar. The microscopic parameters of asphalt mixture were obtained by laboratory tests of asphalt mortar and mixture. The reliability of the modelling method and the microscopic parameters was verified by the DEM simulation of the laboratory tests of the asphalt mixture. Then, the mechanical response of transverse cracks treatment in different geometrical structures under wheel load and temperature load was analysed based on the orthogonal design method. This work concludes that a quadrangular groove with a depth of no less than 6 cm and a width of 60 cm is recommended for treatment of severe transverse cracks. The depth and width of the groove should be increased proportionally in zones where the traffic is higher or the temperature range is larger, but the breadth to width ratio should be less than 15.