How can I disable Universal Clipboard on macOS and iOS?
Disabling Handoff is currently the only way to disable Universal Clipboard.


Mac: Go to System Preferences > General > uncheck Allow Handoff
iPhone: Go to Settings > General > Handoff > uncheck Handoff  


Just so you know, Handoff uses a secure communication channel to transfer information between devices signed into the same Apple ID. 

Data does not travel to Apple's servers or even over the internet. Devices advertise availability to each other via Bluetooth and data is transmitted over Wi-Fi, but only on the local network.