This section of the guide to Destroy All Humans answers the question - what happens after the death of a character or destruction of a spaceship?
If your character dies during story missions, the game will be loaded from the last save. But the save points are scattered - it's never certain whether you'll end up at some point during the mission, at its very beginning, or somewhere, where it won't be even possible to continue.
You can reset the mission at any time and start over.
If you die during exploration or doing side activities, you will simply be respawned on the map.
Consequence of dying
The game doesn't really punish the death of a character. It doesn't take any points or skills away from you. The only problem that may arise is being unable to finish a mission, and that mainly includes boss fights.
Any death in a boss fight will lead you to the beginning of the mission.