My cell phone doesn’t use wifi. Can they stop service to the tower?
Cell towers require power. They could cut the power, so yes.
Other things that could happen:
Inclement weather could bring down cell towers or interrupt power to them. Some have gas generators for such a scenario, many do not.
Marxist government could simply turn the towers off.
Ditto for Wi-Fi, btw. In fact, disabling the Internet would be even easier. Just a few clicks of a mouse and all network accounts are disabled.
Step #2 for a rising dictatorship is to disrupt the people’s ability to communicate. Typically following Step #1, confiscating the people’s weapons.