This may be like killing a fly with a hammer, but my desperate solution was to just use htop to locate and kill the program that locked up my mouse pointer. Sorry, after writing this, I noticed your question explicitly says "without killing it".
Background:
I had the same issue happen to me in File-Roller. I tried to extract a file within an archive by dragging it to PCManFM in Awesome Window Manager. My mouse pointer changed to a grab-pointer-icon, and I couldn't click on anything. It was so frustrating.
Steps to Kill Process:
- Launch Terminal - Hit the hotkeys for launching a terminal, which are
super+enterin Awesome, but are typicallyctrl+alt+tin most desktop environments. - Run htop - type "htop" (without quotes) and press enter.
- Find the Process - In my case, I pressed F3 and typed "roller" (without quotes). This located and selected the file-roller process.
- Kill The Process - Press F9 and select "SIGTERM" to kill the process.
This may not be the best way to do it, but it worked for me and it is easy to remember in a pinch.