There needs to be a network connection between the sending device and the receiving device. No way around that.
For mirroring something streaming from an online source (through cellular), you could set up a “hotspot” on your phone. Then Apple TV can connect to that (just as it would for Wi-Fi) and use that for internet connectivity. And AirPlay streaming would be available (for supporting services).
How to set up a Personal Hotspot on your iPhone or iPad - Apple Support
If Personal Hotspot is not working on your iPhone or iPad (Wi-Fi + Cellular) - Apple Support
Note that not all mobile service providers allow such use for long. There may be a (very) limited data cap on hotspot use, or it may be metered and billed separately. See you carrier’s policy on hotspot use for tv streaming devices.
For almost all long term situations, it is best to get your own home internet connection.