How can I shut off messages from my computer. But I don't want them erased from my phone?

Hi pola273,

You can't delete the Messages app on your Mac, but you can sign out of iMessage.

1. Open the Messages app.
2. In the menu bar at the top of the screen, select Messages -> Preferences. Or, press Command-Comma.
3. Select the iMessage tab.
4. Near the top right of the window, click Sign Out.