I don't believe you can force screen to overwrite the log. It logs to
screenlog.%n by default, where
%n is the screen window number (so each window has it's own log). If that file exists, it appends to it.
However, you can tell
screen to use a different filename, including a timestamp, so you'll get a new log file each time, but you'll then need to manage the old logs.
.screenrc you can put the following line,
to create log files that include the window number (
%n) and the year, month, date, and time.
Alternatively, you could create a
bash alias that deletes the log file before running screen, for example,
alias screen='rm /path/to/log; screen'
If you want to affect
screen log files in the current directory, just remove
/path/to/log/ from the commands above.
Lastly, depending on what you're trying to achieve, the Linux tool
script might be more useful than just logging in
man script for more information.