Heavy-duty hexapod robots are well-suited for physical transportation, disaster relief, and resource exploration. The immense locomotion capabilities conferred by the six appendages of these systems enable traversal over unstructured and challenging terrain. However, tipping can be a serious concern when moving with a tripod gait in these challenging environments, which may cause irreversible consequences such as compromised movement control and potential damage. In this paper, we focus on heavy-duty hexapod robot sideline tipping judgment and recovery during tripod gait motion, and a novel sideline tipping judgment and recovery method is proposed by adjusting an optimal swinging leg to the stance state. Considering the locomotion environments, motion mode, and tipping analysis, the robot’s stability margin is quantified, and the tipping event is evaluated by the Force Angle Stability Measure (FASM). The recovery method is initiated upon detecting that the robot is tipping, which involves the selection of an adjustment leg and the determination of an optimal foothold. Since the FASM is based on the foot force and robot center of gravity (CoG), the stability margin quantification expression is reformulated to the constraint form of quadratic programming (QP). Furthermore, a foot force distribution method, integrating stability margin considerations into the QP model, has been devised to ensure post-adjustment stability of the landing leg. Experiments on tipping judgment and recovery demonstrate the effectiveness of the proposed approaches on tipping judgment and recovery.