Big problem with 1994 Miata
 

Hey guys I'll try to explain as much as I can. It's a 1994 Miata 1.8L Automatic. The problem with the vehicle is, when you put it in reverse it wont move at all until you heavily push down on the pedal and then it will start rolling. Same goes for accelerating, you really have to press the gas then it'll barely start moving it will start shaking badly and slowly start accelerating and once it gets to about 25-30MPH it will start to get power. Also when I'm driving it on the highway, as soon as i get off the highway and come to complete stop it shuts off completely, but it will start right back up. The car was bought a few months ago, never had a problem other then a radiator leak which was replaced.

Any help is appreciated thank you.

Sounds like something timing/ignition related. I'm very new to these cars so don't take my word for it. I personally would give it a simple tune up with plugs and wires and check the timing once the new plugs and wires are in. Somewhere to start

Does the engine run well or not? I'm having trouble deciding if you are having transmission problems or if the engine is barely running from your description. Clarity is our friend when it comes to diagnosis. You aren't being charged by the word here or anything.