It depends on what your hunting regulations are in your state on draw weight.
As far as a 40lb recurve killing a deer....yeah, it will kill a deer. Make a good shot, with a good fixed blade head and you will have a dead deer every time.
Broadheads are scary lethal, they sometimes kill faster that a bullet, with a heart/lung shot.
side note: Dont over bow yourself, pick a light enough weight you can develope good form with. You can always upgrade your limbs later down the road. I know this from experience, I chose a 50lb recurve to start with and was humbled real quick (I shoot 70lb compound). I was frustrated to say the least and had absolutley no consitency. I was ready to quit, I eventually broke down and bought a samick sage in 30lbs and have been working with that. I am ready to upgrade my limbs and I am going to get some 45lbers and call it good.