If an instant or sorcery spell destroys Dryad Militant directly (like Murder does), that instant or sorcery card will be put into its owner’s graveyard. However, if an instant or sorcery card deals lethal damage to Dryad Militant, Dryad Militant will remain on the battlefield until the next time state-based actions are checked, which is after the instant or sorcery finishes resolving. The instant or sorcery will be exiled.

If an instant or sorcery card is discarded while Dryad Militant is on the battlefield, abilities that function when a card is discarded (such as madness) still work, even though that card never reaches a graveyard. In addition, spells or abilities that check the characteristics of a discarded card (such as Chandra Ablaze’s first ability) can find that card in exile.