The application of active deconstruction schemes to manage nuclear waste has long history as a proposal, but has not yet been demonstrated as technologically practical. The usual schemes (i.e. the ones people have put time and money into and are still looking at) use electron beams (either directly or as a bremstrahlung source) because electron beams are easy and relatively efficient to make.
The underlying technological problem with your idea is the line
Accelerate neutrons to as high energy as possible [...]
because there is no simple way to accelerate neutrons. Our accelerators work on charged particles. Neutrons beams have to be generated as a side effect of some other process and that adds a completely unnecessary inefficiency to a process already of marginal efficiency.