WHAT to do with a deaf dog?

a holes are always dumping off dogs where I live (outskirts of town). My son saw ( i told him get the plates next time) the guy dump off a a cute white lil pup. come to find out she is deaf as a door nail. Ok that dog goes nuts after people , cant house break her, runs off and chases anything...im sitting here like a butt yelling at it to come back ...duhhhh it can't hear. if i turn it in to S.P.C.A. they will put her down for sure but i can't control her what to do? thanks