How to remove the white border from PDF converted through word?

Is it possible? Yes. Anything that can be done with manual procedures can also be done automatically. The question is: how are you doing it now? If you are saving from Word as a PDF, it is possible that you can create a VBA macro in Word to accomplish the same task with a single key combination. The initial macro can simply be created using the macro recorder then manually tweaked in order to complete the automation task at hand. Again, in order to do this, one needs to know exactly how it is currently being done first.

If this happens when you "save for web" then you probably have your matte color set to white. When you are in the Save for Web dialog box, look over to the right where it says "Matte:" Make sure that is set to None. If this makes your artwork look choppy around the edges set a matte color that is the same as the background color of your webpage.

Select the white border with the magic wand :MagicWandTool: (lower tolerance so you only select the border) then invert the selection with CTRL + I. Finally press CTRL + Shift + X to crop to the selection.

Save in your preferred format.