Restart App and Restart Mac
Try to quite iMessage application from the top left corner X button on Mac and reopen and send an iMessage. Restart Mac by click on the Apple menu and restart.Check the Internet is working on Mac
Make sure to check that the Internet is working on Mac. Once the Internet is connected, try to browse a page and make sure the Internet is working.Check the Date and Time in your Mac
Sometimes, due to incorrect dates and time on Mac, iMessage does not work properly. To correct the date and time on Mac, follow these steps.Apple menu > System Preferences > and then Date and Time. Now add a check mark to "Set date and time automatically." If it checked, leave it there.
Sign out and Sign-in back iMessages
Open the messaging app and go to Preferences on the menubar. Now click on sign out. Now sign in with Apple username Password.Check the iPhone and Mac iMessage configuration are the same
On the iPhone, go to Setting > Messages > Send and Receive.On Mac go to Messages > Preferences > Accounts > iMessage Account. Both account details must be the same.
Due to an incorrect configuration, iMessage does not work correctly on Mac. Therefore when you configure iMessage on Mac, Make sure to add correct details that are included in the iPhone iMessage setting. Also, make sure to use a good internet connection because a slow internet connection makes some issues on requests.
Read: How to Get iMessage for Windows by Using Chrome Remote Desktop
How to Turn off iMessage on Mac