PlayStation Vita will either save internally to the game card or to a separate memory card. But not both.
Whether a Vita game uses internal memory or a separate memory card is at each individual developer's discretion.
When a Vita game does require a separate memory card, you'll need one inserted from the outset to play.
In a previous, unconfirmed report, Kotaku Japan (translated by Andriasang) listed both the Vita games that save internally to the game card, and those that require a separate memory card. The latter included eye-catchers like Uncharted: Golden Abyss, Disgaea 3 Return, Ridge Racer, Everybody's Golf 6, Dream Club Zero and Monster Raider.