The axons that have been disconnected from their cell bodies will die. This takes place over a period of days or even weeks.
However, the cells that the axons contact usually are not killed, unless they have been directly injured by the mechanical trauma. Likewise, the cells that the axons come from also usually survive the axonal injury unless they are close to the injury site.
The cells above and below the injury site are still connected with each other. In fact, after any injury, many of these cells develop new connections to each other, possibly accounting for spasticity.
Likewise, some of the cells above the injury site develop new connections to each other, possibly account for neuropathic pain.