How do I dispose of a corpse?

Use the console

As with previous Bethesday games, the markfordelete or disable console commands can be used to force an entity to despawn. Using markfordelete may be safer as there are some indications that using disable will not remove the object from the world state in your savegame. The former is also less likely to bug out as it should follow the default cleanup behaviour.

Via the Wiki:

markfordelete - Similar to disable, will delete any item from the game, removing it permanently. It may disappear immediately, or it may require you to exit and re-enter the area.

While I haven't confirmed this myself, using the console apparently does not disable achievements.

if you have running water nearby you can drag the corpse there and watch it float away

Build a small shack and drag all bodies there?

=Build a graveyard.