1992 Chevy Corsica 1992 corsica shuts off

I have a 92 corsica that starts and runs fine for about 20minutes to a half an hour then when u go to stop it kicks and bucks and shuts off.If u sit there for 10 minutes you can drive it for awhile till u slow down to stop again.If you drive it on the highway its fine and acts as if nothing is wrong UNTIL you were to get off at an exit and slow down.I am not a mechanic but have worked on cars some and it reminds me of driving a manual car and trying to stop it when its in a high gear.To me it feels like maybe its not downshifting? maybe a switch is bad? in the tranny?I down deep feel its a tranny issue. Iv had people tell me its fuel but that makes no sense to me because u can drive all day till u run out of gas or slow down on a highway,anyways im at a standstill.Thanks