I've never hunted with a sling but I think I'd need a lot more practice if I was to hunt successfully. (As a caveat I'll say that it is extremely likely that slings are illegal as hunting tools in the UK, before anyone suggests it!).
At a range of 40-50 feet I can accurately hit an object about 5-6 feet square with a rock of a size of a duck/goose egg. This would probably not be travelling with enough force to knock out/kill an animal that has a target size of 6 feet square, such as a deer, unless I was very lucky with my aim! It would be fine for something like a rabbit, but then I'd have no chance of hitting it!
In a survival situation, If all I had was a sling, then I'd probably use an old Native American technique which was used for hunting waterfowl. They used a sling loaded with a mass of rocks, or a bundle of small darts or arrows. they would stand on the shore of a lake where a flock of birds had settled, and 'sling' upwards over the flock, dropping the load onto the birds. with luck one of them would hit their target, and they could then swim out to retrieve their kill. There are more details online but I can't remember what this type of hunting/tool was called.
However, the best bet would probably be a bow and arrow - potentially harder to make, but a much more reliable hunting tool that requires less practice to use accurately than a sling.