We develop an impulsive dynamical-systems model for constrained woody-plant growth under root restriction, periodic pruning, and mechanically induced growth suppression, using bonsai as a tractable case study. The model couples a physiologically grounded root–shoot–auxin compartment system with a pot-volume carrying capacity and discrete pruning impulses, yielding an analytically accessible framework in which dwarfing emerges from explicit source–sink constraints rather than genetic modification. Within this setting we derive a pot-bound equilibrium strictly dominated by the corresponding free-tree equilibrium, obtain a minimum viable pot size for sustained positive shoot biomass, identify a critical pruning interval below which the maintained periodic orbit collapses, and predict a departure from classical 3/4 allometric scaling at finite pot sizes. The formulation is species-agnostic, but its parameters admit direct biological interpretation and support numerical calibration. Beyond bonsai, the paper provides a compact mathematical theory of constrained woody-plant growth under repeated discrete intervention. MSC Classification: 34A37 , 34D20 , 92B05 , 92D25