I have the same issue and couldn't find an answer either. The problem is that the Apple TV requires an internet connection if you want to AirPlay internet content from your iPhone to the Apple TV, e.g. if the Apple TV isn't connected to the internet somehow, then Netflix or Youtube won't AirPlay from the iPhone to the Apple TV. I don't have a "house" internet connection currently, and when I bought my iPhone I was assuming I just can use my unlimited data plan to watch Netflix movies on the iPhone and AirPlay it to the big screen. No luck here, yet!!!
You can use the iPhone Hotspot and connect the AppleTV to that Hotspot, but I have a 5GB limit and that will be depleted with 2 movies or so, so that doesn't work either. I also can use the Hotspot to connect to my MacAir, which works great and 5GB limit is not the issue if you don't use it for movies, online gaming etc. But you could run into issues if you have to download big files, like updating the OS etc. That is something you have to consider when you are cutting the home internet.
I tried to somehow have the Apple TV use the Hotspot internet connection to just have access to the internet but use the iPhone unlimited data plan to stream movies, but the problem is that Apple TV can only connect to 1 WiFi network at a time and while it is connected to the hotspot, you can't connect to another network for AirPlay your content. Also, the ethernet port on the Apple TV (if used) will be prioritized and then WiFi would be turned off, ruling out the possibility to use ethernet and WiFi simultaneously to have one connected to the network using AirPlay and one using the Hotspot internet access. I believe the real problem is that the Apple TV needs internet access (for verification purposes???) while using AirPlay, and if there is no internet access through the network you are using for AirPlay, it might not work, at least I couldn't find a solution for it yet.
I was reading that with iOS 8 there might be a new feature that uses Peer-to-Peer technology between iOS devices and Apple TV, that might enable that you can connect to Apple TV with Peer-to-Peer and also connect it with the iPhone Hotspot for internet access (I would assume that the data amount from just being connected to the internet would be minor if the streaming data comes from the data plan itself from the iPhone).
That said, I can still stream content from my iTunes library to Apple TV, which is stored on my computer and doesn't need to be downloaded or streamed (Not the content I have purchased. Some folks mentioned bought content still needs internet access). So you can use your content you already have on the computer by using your local network. I hope somebody can give a solution to that problem! I was hoping to never have to deal with cable or telephone companies ever again, just using my mobile carrier, but I might be out of luck!
P.S: I also tried to connect my MacAir with the iPhone hotspot and then share this internet connection from the MacAir with my Apple TV. Didn't work either :-(