As long as the system is writing to a log file, you cannot modify or erase it. Once you rotate the log file and the system starts on a new one, you can delete the old one if you wish. You can read your log files even if they have not been rotated, you just can't delete them while a server is still using them.
You can access and delete your old log files via FTP by looking in the "/logs" directory of your site. Via ssh or SFTP, this is the /home/logs directory. (But you'll still have to rotate them before you can do anything but look.)
If you've disabled logging, the option to rotate them will not be available to you. Enable your logs, rotate them, disable them, and then delete them.