We established a 3D coupled model to study the electromagnetic-thermal behaviors of a levitation system containing a bulk high-temperature superconductor (HTS) with a cuboid slot under the nonuniform magnetic field due to the movement of a permanent magnet (PM), analysing the influences of the geometrical parameters of the slot and inclination angle on the electromagnetic-thermal behaviors, giving the dynamic distribution of the global electromagnetic force density in the HTS. The results show that the longer the length of the slot, the smaller the levitation force, and the greater the loss. As its length takes up 7/10 of the HTS diameter, the loss is 4 times that of the HTS without damage. Due to the homodromous induced current appearing near the slot, the maximum guidance force increases with the length. The levitation force decreases with the increase of the slot depth. Its curve near the maximum becomes blunt and the loss increases significantly. As the depth is 3/5-4/5 of the HTS height, the loss is 300-400 times of that without damage. The guidance force and loss increase with the depth. As the inclination angle rises, the levitation and guidance force both drop. At 30 • , their maximums decrease by 70 % and 90 %, respectively. The lateral stability of the system thus becomes poorer, indicating the inclination angle is one of the important factors for instability. As the PM moves vertically, the guidance force density symmetrically distributes near the both wide sides of the slot. Its side faces with the wide sides will bear the shear force, resulting in that the slot has the tendency to tear along these faces. As the PM reciprocates laterally, the slot is subjected to the lateral shear force, proportional to the displacement.