Most devices could can have a proxy set on them which would be invisible to the application. Personally I use proxydroid (or similar) on android and IPtables on iPhone. Your devices may need to be rooted (and any apps patched to avoid root detection). You will also come up against certificate pinning like you would over a WiFi connection and will have to patch the application to bypass this. (unless you have the private key for the target's SSL cert - which is unlikely unless you are the sysadmin for the target server)
Over a 3G / 4G connection, you would need to run your proxy server on a machine with a public facing IP address - VPS servers are useful for this.
Alternatively you may be able to get the phone to VPN into a network that you control and pass it fake DNS information using DNSMasquerade or similar - you can set up a server with your proxy operating on ports 80 and 443 and give the IP to that server as the response to any DNS request made by the phone. (some more complicated layer 3 routing may need to be done if the App uses IP addresses directly)
You can't transmit / receive data on the radio bands allocated to 3G / 4G under most jurisdictions due to wireless telegraphy laws. If you want to spoof a 3g / 4g network without violating any laws, you could set up a faraday cage (use a certified commercial solution), set up your own base station using an SDR and openBTS or similar and sniff / proxy the traffic from the role of the mobile network operator (any GSM / UTMS / 4G encryption on the channel will be done using your parameters but you will still have to MitM any higher layer (HTTPS etc.) traffic. This works in most cases, though check with local laws / an experienced lawyer in your jurisdiction first. The hardware to do this can be expensive.
Using a hacked commercially available femtocell may be a simpler way to do this though this probably still violates many laws and most likely your user agreement with the network operator. Proceed with caution. MNOs actively monitor attempts to circumvent protections on their devices and employ third party consultants to try and break their security. Some may use VPN connections back to the MNO, though I have not examined enough to fully confirm or deny this. An past example of this approach is here, though note that you will still need to break the HTTPS encryption / tell your device to send the traffic to a proxy. Hosting your proxy server on a public IP address or using your own VPN is probably a much simpler (and legally safer) approach. https://www.nccgroup.trust/globalassets/newsroom/us/blog/documents/2013/femtocell.pdf