This work presents an approach for dealing with suspended-cable load transportation using unmanned aerial vehicles (UAVs), specifically when the cargo overcomes the lifting capacity. Herein, this approach is referred to as the Side-Pull Maneuver (SPM). This maneuver is an alternative and viable strategy for cases where there is no impediment or restriction to dragging the load along a surface, such as with pastures or marine environments. The proposal is based on a joint observation of the thrust and altitude of the UAV. To make this possible, the high-level rigid-body dynamics model is described and represented as an underactuated system. Its altitude-rate control input is then analyzed during flight. A flight state supervisor decides whether the cargo should be carried by lifting or by side-pulling, or whether it should be labeled as non-transportable. Comparative real experiments validate the proposal according to which maneuver (lifting or dragging) is performed for transport.