What are you talking about, pruning, cuttings, or (I suspect) girdling for an air/ground layer? Since you say 'cuts' it is only clear that we're not talking about a tourniquet girdling a stem.
If you are girdling a stem for an layer, you remove everything outside the wood (xylem).. The amount of swelling that subsequently occurs is pretty much out of your control as it is a consequence of the cellular DNA. Interrupting the polar auxin transport stream causes auxin to accumulate above the point of interruption. The accumulation of excess auxin causes the production of ethylene. Ethylene causes enhanced radial growth - how much is controlled by the DNA. Clearly one might enhance the effect by applying a high concentration od rooting hormone (an artificial auxin), but how much this enhances radial growth is again controlled by the DNA. Further, too high a concentration becomes toxic, xo tissue will die from the point of application go a point where the DNA can cope. In my experience it requires some careful measurements to observe the added effect.
Yada, Yada, Yada.