Should I remove the 2x4 between the joists of this deck?
I see no reason for that board, but a photo would help clear things up. I also assume that the joists are hung on the beam using standard steel hangers and approved fasteners. If all that is correct, you should be able to remove the board. 

I'd guess that it was added to support decking joints that fell over the beam. Presumably the decking ran parallel to the beam. A better approach would have been to put individual blocks in that essentially carry the joist through the beam gap.