Probably the best way to practice for hunting game animals is to actually purchase some 3D targets that represent the game animals you will be hunting. You can find some pretty good deals on 3D targets at places like cabelas, bass pro shops, or even yard sales. I recommend buying as many as you can afford, or if they are cheap buy a few because if you shoot as much as me you will go through several targets. I like to place 3D targets in wooded areas that are similar to the areas I hunt. I also like to shoot from my treestand giving me the best practice for actual hunting situations.
However, practicing hunting situations is not always an option, this is why stump shooting is such a great tool. Stump shooting is exactly what it sounds like. I like to walk through the woods with my hunting buddies and shoot at dead rotted logs or stumps. Because they are soft the logs do not harm your arrow. A good tip to use when stump shooting is the zwickey judo point. The judo point forces your arrow to pop up when hitting the ground keeping it from burrying under grass or leaves. However using a regular field point will work just fine as well.
If you do not have a woods that you can stump shoot in and cannot purchase any 3D targets then you can shoot your recurve at other objects as long as you do it safely. Sometimes I will head to my backyard and shoot at anything from old basketballs, tennis balls, dirt clods, or even bottle caps. Always remember to be safe when practicing. Practicing often will help you become a proficient archer with traditional equipment!