In Savage Worlds Deluxe, when a vehicle goes out of control does its speed drop to zero?
Not necessarily, but it is possible.
There are two ways to resolve a vehicle encounter: With a Chase or with the rules under Vehicles
Since you asked about going “out of control”, I'll cover the vehicle section first, as that is where that wording appears.
According to the Losing Control section of the Vehicle rules on page 114
Failing a Driving roll causes a vehicle to go “out of control.” When this happens, roll 2d6 on the Out of Control Table. Resolve any additional movement (such as slips or flips) immediately. Anything in the way gets smashed — check out the collision rules above if that happens.
Out of Control
On a roll of a 2d6
12: Flip: The vehicle flips end over end 1d4 times. Move it forward that many increments of its own length. Roll collision damage for the vehicle, its passengers, and anything it hits. Slow and heavy vehicles such as tanks (GM’s discretion) don’t flip but suffer a Slip or Skid instead.
On to the Chase rules, which begin on page 94.
Basically, the Chase rules are complicated, so I'll try and hit the relevant rules to your question.
During a chase - especially when attacked you might become shaken.
Shaken Characters: If a character driving or piloting a vehicle is Shaken, he must make an Out of Control roll (see page 115). If the vehicle suffers damage, calculate it at half the vehicle’s Top Speed (see page 113). Characters who are Shaken at the start of a turn make their maneuvering Trait roll at –2. They attempt to become un-Shaken on their Action Card as usual.
On that maneuvering Trait roll. If you draw a complication:
Disaster: Make a Trait roll at –4. If the roll is failed, the character suffers a disaster of some sort—a car hits a solid obstacle at its top speed, a runner falls off a ledge, etc. Where this isn’t possible, the runner gives out, the vehicle stops, etc. In any event, this participant is out of the chase.
So the upshot is, there is a chance that the vehicle will come to a dead stop when it goes out of control, especially if it hits something.