1997 Dodge Neon Loses power when slowing down

When cranking the car one must push the gas petal to keep the car from shutting off. Once car is in motion it runs fine, until you get to about 10 or 15 mph on slowdown. The car then shuts completely off except for the radio and lights. I also lose power steering. I have purchased a new battery and taken it to the mechanic and they can find nothing wrong with it. Before the car shuts off it jerks almost as if it isn't getting enough gas.