Leaves as caterpillars and nectar as adults are what spicebush swallowtails eat.
Specifically, the swallowtail in question (Papilio troilus) goes through two main feeding stages. The leaf-eating larval stage is less picky in its choice of food sources than the nectar-sipping adult. As a butterfly, the spicebush swallowtail prefers nectar from honeysuckle, jewelweed, and Joe-pye weed.