We present neutron-scattering results on the magnetic excitations in the spinel compounds Lix [Mn1.96 Li0.04] O4 (x=0.2,0.6,0.8,1.0). We show that the dominant excitations below T~70K are determined by Mn ions located in clusters, and that these excitations mimic the dynamic scaling found in quantum critical systems that also harbor magnetic clusters, such as CeRu0.5 Fe1.5 Ge2. We argue that our results for this classical spinel compound suggest that the unusual response at low temperatures as observed in quantum critical systems that have been driven to criticality through substantial chemical doping is (at least) partially the result of the fragmentation of the magnetic lattice into smaller units.