Screen shot drop down menu with snipping tool

Whenever I've needed to do this, I set a delay on the snipping tool - usually between 3 and 5 seconds.

This gives me enough time to click on "New" and then open the drop-down menu before the screenshot is taken.

The delay feature only works for the Windows 10+ version of the snipping because it wasn't introduced until then. For earlier versions, you need to use the cntrl-PrtScr option. Open up the Snipping Tool. If it's active to create a new snip, click cancel or hit the ESC key. Open up the desired menu and press cntl-PrtScr, this will reactivate the Snipping tool but leave the menu open. Then you can select what kind snip you want to make (free form, rectangular, window or full screen) and grab your screenshot.