I'm sure it would but there are questions. One is what is your state game laws on the subject. I doubt the .40 S&W would qualify in Kansas, but I'd have to look at the laws again to be sure. The smallest commonly encountered deer is normally a Whitetail. The .44 Magnum is really less powerful than a 30-30, which is kinda considered a minimum caliber for sport-hunting. The .40 is considerably less powerful than the .44 Mag. Lots of deer have been taken with the .357. OTOH though, lots of handgunners consider it to be pretty weak. If I was hunting Whitetail, I'd want a .41 Mag. level load or stronger.