Erosion, as a key control of landslide dynamics, significantly increases the destructive power by rapidly amplifying its volume, mobility and impact energy. Mobility is directly linked to the threat posed by an erosive landslide. No clear-cut mechanical condition has been presented so far for when, how and how much energy the erosive landslide gains or loses, resulting in enhanced or reduced mobility. We pioneer a mechanical model for the energy budget of an erosive landslide that controls enhanced or reduced mobility. A fundamentally new understanding is that the increased inertia due to the increased mass is related to an entrainment velocity emerging from the inertial frame of reference. With this the true inertia of an erosive landslide can be ascertained, and its control on the landslide mobility. This makes a breakthrough in correctly determining the mobility of the erosive landslide. Erosion velocity plays an outstanding role in regulating the energy budget and decides whether the landslide mobility will be enhanced, reduced or remains unaltered. This depends exclusively on whether the energy generator is positive, negative or zero. This provides the first-ever explicit mechanical quantification of the state of erosional energy and a precise description of mobility. This addresses the long-standing scientific question of why many erosive landslides generate higher mobility, while others reduce mobility. By introducing three key mechanical concepts: erosion-velocity, entrainment-velocity and energy-velocity, we demonstrate that the erosion and entrainment are essentially different processes. Landslides gain energy and enhance mobility if the erosion velocity is greater than the entrainment velocity. The energy velocity delineates the three excess energy regimes: positive, negative and zero. We introduce two dimensionless numbers, the mobility scaling and erosion number, delivering an explicit measure of mobility. We establish a mechanism of landslide-propulsion providing the erosion-thrust to the landslide. Analytically obtained velocity indicates the fact that erosion can have the major control on the landslide dynamics. To prepare enhanced modelling of entrainment-related mobilization, we also present a full set of dynamical equations in conservative form in which the momentum balance correctly includes the erosion-induced net momentum production.