I assume you are using an older build of eduke32 on windows. I've had similar problems earlier. After starting up eduke32, do not switch to other programs/windows until you see the title [full]screen of the game. Or ALT-TAB to other programs and back when your problem occurs _after_ the title screen has loaded.
Or use a somewhat current build, like:
http://dukeworld.duke4.net/eduke32/synthes...100425-1623.zip
At least for me this has fixed that mouse issue. There are newer builds available but they might not work as you expect.
Please post further questions here:
http://forums.duke4....hp?showforum=27