Severing roots out of purpose is hardly ever something that an arborist would find desirable, though it nonetheless occurs rather commonly where construction takes place and also where abatement of nuisance is practiced for terrestrial encroachment of a tree.

Current research indicates that the severance of roots is, by-and-large, highly variable. In one instance, root severance may have very little adverse impact on tree stability, though in other cases may weaken a tree by over 20%.

Roots that 'guy' a tree (exist uphill of the trunk) or reside on the outer (tension) side of a lean are ultimately far more crucial to the tree than the majority of the remaining root crown. Severing roots may not therefore simply be a case of "no more than 25% of the root crown can be lost", as context is key. If a guying / tension root is severed, the impact upon stability will be far more significant than if a compression root (or even multiple roots) is lost.

Statistically (from a survey done on willow oak), when assessing strength loss due to buttress root severance at the base of the trunk, a loss of 50% of the buttress roots will reduce the mechanical required force to move the tree one degree by a third (33%). However, due to the oscillating nature of winds, such a loss in root mass will result in a much higher decline in strength, particularly for larger trees with more wind sail (or where root decay is evident). Interestingly, such a loss can at times be achieved simply by severing a single guying / tension root, which suggests that trenching may be of particularly significant adverse impact to trees in more exposed sites.

Additionally, research indicates that severing roots closer than at a radius three-times the trunk diameter is not recommended, as tree stability declines significantly once this threshold is surpassed.

Source: Smiley, E. (2009) Root pruning and stability of willow oak. In Watson, G., Costello, L., Scharenbroch, B., & Gilman, E. (eds.) The Landscape Below Ground III. USA: International Society of Arboriculture.