Hi,
That aspect of the monitor can't be controlled by the OS, you might be able to find an option in the monitor's menu system that will make it turn off after a certain period of inactivity over HDMI, but it sounds like the monitor is just acting like a normal TV when you use the HDMI connection - i.e. still on, just displaying a "no signal" screen and waiting for the connection to be re-established.
I'm sorry I can't help you further...
You could try using a HDMI>DVI converter and routing the HDMI lead through the converter and into the DVI port of your monitor?
Banjo