You're not supposed to stop it. You have to activate the lift to the panel by going to the cab room by the stairs you have to go down. There's a man in there under the light you have to kill, it's easy to just sneak up behind him. When you've activated the lift go to the ground floor, turn the valve on the bottom of the missile and take the lift in front of the rocket, it'll take you up a level where a panel on the rocket will now be open. Hack that, the right numbers come up within about 8 seconds of the 30 second timer starting . when you've done that go up the ladder to the right and then run left to the rope hanging from the ceiling and use it to complete the mission.
All times are (GMT -08:00) Pacific Time (US & Canada). Current time is 3:45:43 PM