The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of molecular dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with L segments, consisting of breakable bonds, along with two side chains of length N, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond lifetime decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains N = 1-4. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The lifetime declines with growing contour length L as proportional to L-0.17 and with side-chain length as proportional to N-0.53. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length L(t) of the fragments with elapsed time indicates the possibility that two different mechanisms may govern the fragmentation process.