The Mothership is the psychedelic Camper owned by The Truth. During the mission Black Project, the Mothership is completely indestructible (except the never-fail methods of sinking it in the water, flipping it over, etc.), and if you can manage to get it to a garage, it will retain these qualities.
Go through the mission until you get the jetpack. Instead of going to meet The Truth, fly over to Doherty and get in the crane behind CJ's garage. When you get out, the Jetpack is gone and you once again have control over your arsenal. However, you have no ability to enter any vehicle.
You will have noticed by now that there is no traffic, very few pedestrians, and very few spawned cars. Find any vehicle and drive back to the Area 69.
Once you arrive, find the small airstrip on the eastern part of the base. You should find there at least one Rhino parked in a hangar near the airstrip. Take one and drive to The Truth meeting point in Arco del Oeste.
When you arrive there, make sure you don't drive onto the red marker as doing so will complete the mission.
Push the Mothership using the Rhino towards the Verdant Meadows airstrip. Note that the Mothership may land face-down and explode. Don't worry about it, as this does not affect the Mothership itself and does not fail the mission. Once you get it into your garage/hangar, it'll be good as new. Once this is done, kill yourself with the grenades to fail the mission. (Tip: if The Truth is still in the Mothership, which he may be, make good and sure you've wedged the Mothership into the corner, or he will try to drive away when you die.)
You'll spawn in Las Venturas; drive on back to the hangar, verify that the Mothership's in the garage, go ahead and shoot the gas tank if you want to make sure it's really invincible, and save your game.
Note : During this mission, the wanted level is locked, so you may want to explore San Andreas and attempt to collect oysters inside Easter Basin Naval Base or other collectibles in restricted areas before killing yourself.