In TextMate I can do use a keyboard shortcut to pull text up to the cursor as shown in attached gif. Can I make a macro that will do this in Microsoft Word?
I don't think native KM can do that, but Word VBA should be able to, and AppleScript might be able to. But it is a fairly complex workflow, so it will probably take some trial-and-error.
Here's where I would start. This is an untested idea.
Find out if there is a Word command, menu item, shortcut key, etc, that will select to the next non-blank character. You might look at the Word Find feature.
If there is then you've got it -- just select from cursor to next non-blank char, and delete.