Electron removal in collisions of alpha particles with neon dimers is studied using an independent-atom-independent-electron model based on the semiclassical approximation of heavy-particle collision physics. The dimer is assumed to be frozen at its equilibrium bond length and collision events for the two ion-atom subsystems are combined in an impact parameter by impact parameter fashion for three mutually perpendicular orientations. Both frozen atomic target and dynamic response model calculations are carried out using the coupled-channel two-center basis generator method. We pay particular attention to inner-valence Ne($2s$) electron removal, which is associated with interatomic Coulombic decay (ICD), resulting in low-energy electron emission and dimer fragmentation. Our calculations confirm a previous experimental result at 150 keV/amu impact energy regarding the relative strength of ICD compared to direct electron emission. They further indicate that ICD is the dominant Ne$^+$ + Ne$^+$ fragmentation process below 10 keV/amu, suggesting that a strong low-energy electron yield will be observed in the ion-dimer system in a regime in which the creation of continuum electrons is a rare event in the ion-atom problem.