If you're running on 1.0.x, then there's no way to configure the rollover of logging.log. You can redirect the console output as you normally would when launching a process, e.g. to direct it to a file, or to /dev/null if you just want to refer to the file.
We've improved this area of dm Server considerably in the latest 2.0 nightly builds. The config/serviceability.xml file controls the configuration of LogBack which is now used by dm Server under the covers. This means that, in 2.0, you can configure the output pretty much however you like, e.g. you can disable the console output simply by remove the reference to the ConsoleAppender.