I am using a spoofed MAC address and Tor services for spoofing my IP address.
Will it make any difference if I am using the phone's internet by tethering? Will that compromise my anonymity? If so, how could I get around it?
I does not mather how you connect to the internet if you use Tor. The traffic will be encrypted anyway, so whoever controls the network you use - be it your ISP or your cell phone provider - will not be able to read it.
However if you do it by tethering, your cell phone company can see that you are using Tor and could potentially block it (just like your ordinary ISP would if you connected with your ordinary broadband).
Do note that MAC spoofing has nothing to do with this. Your MAC address never leaves your local network so there really is no point in spoofing it to stay anonymous on the internet.
Also, I would not call using Tor a form of IP spoofing.