I've done a bit of what you're intending to.
First, use a kinetic bullet-puller to pull the bullet from the case.
Pour out and discard the powder. Remember, it's highly flammable.
Remove the primer, very carefully, by gently tapping it out with a depriming tool from a Lee Loader, or use a reloading press if you have one to deprime the case. Remember, the primer is highly volatile.
If the anvil is loose in the primer, you can remove it with a wooden toothpick, and using the toothpick, loosen the priming compound and discard it. Otherwise, you can "remake" a fired primer into an unfired-appearing one by removing the anvil, then using a flat pin punch on a flat steel surface (like a vise) to pound it flat. You can re-seat it into the case with a loading press or a specialized priming tool, such as the Lee priming tool.
You can remove the lead from a jacketed bullet by holding it with a pair of tongs in the flame of a butane torch or similar heat source. That will leave you with an empty jacket.
If you're looking to lighten a hollow-point or TMJ bullet, you can saw the base of the bullet off with a hacksaw, then melt the core out. If you're trying to lighten a soft-point bullet with exposed lead at the tip, you can use this same procedure, taking care to not heat the tip of the bullet enough to melt the lead in it.
Finally, you can use a reloading press to re-insert the empty bullet into the empty case. Recommend you drill a hole or two in one side of the case (where you may be planning to mount the mounting hardware) so that it will be clear upon close examination that the round is a dummy.
Good luck!