Exporting animated gif - limiting to the size of artboard

Blank Space?  Transparent space  or a solid color border.  The canvas size of the animated gif should be the same size as your document's canvas size or the size you resize the animated gift to.  Save for web does not trim transparency or color borders.

Save for web has problems with artboards, probably because it’s old and developed before there were artboards. I’m guessing that the exported animated gif is increasing in size because it is ignoring the mask on the background image. Export As was developed to work with artboards, but unfortunately it doesn’t do animated gifs, at least not yet. I think you need to move all of the elements out of the arboard and delete the artboard. Then crop your document if needed to the size required. I expect that save for web will work fine after you do this. Let us know.

You can drag all the layers in the layer panel out of the artboard, or you can duplicate the layers into a new document created at the correct file size. That might be the easiest.