Stop it at a sign or light, then go to accelerate, it cuts off?

So, I drive around for work. After a few hours of driving. It'll start up fine, then when I slow down enough or stop at a sign or light, then go to accelerate, it cuts off. It's trying to stay on, and RPMs are going up and down but doesn't move at all then it just shuts off. I crank it up again let go of the key and it continues to try to crank for 5 seconds and then starts up again. It rides fine till I stop then it cuts off. If I don't slow down (ex: on highway) it won't cut off until I slow down or stop and go to accelerate. I could drive it if I didn't have to stop. But in Miami traffic is impossible. Please help me. I keep putting money into it. Just changed the O2 sensor. Engine light cut off. Then cuts on, and when it starts happening again. And it will disappear.