Open the Messages app on your Mac
Select the conversation you want to clear
Right-click the message or conversation
Click Delete
Confirm the deletion if prompted
To delete multiple messages, hold Command and click each message
Press Delete or right-click and choose Delete
To clear an entire conversation, select it in the sidebar
Press Delete on your keyboard
Confirm the deletion if prompted
To remove all messages from iCloud, open Messages
Go to Messages in the menu bar
Click Settings
Click iMessage
Turn off Messages in iCloud if needed
Delete messages on other Apple devices if they sync through iCloud