You can clear logs at any time by selecting Tools > Clear Logs. Choose the log you want to clear from the secondary menu. There are three types of logs :
You can set the amount of logging the Server Manager will maintain in Tools > Options > Server Options > General > Logging level.
Select this option to clear all the logs described above.
Once you've chosen the log you want to delete, you are asked to confirm clearing of the log. Click Yes to clear it and No to return to Server Manager without making any changes.