Don't cut them apart after the first sewing down the diagonal. Cut on the opposite diagonal to the one you've sewn down first and then cut on the line you drew. You'll have mirrored pairs that way and less sewing.
I have also drawn both diagonals and sewn to the center--stopped and moved 1/4" to the other side of the line and continued to the corner. Turned the block and done the same thing again to get matching instead of mirrored pairs. For an Ohio Star--either way will work but the mirrored version is fewer steps and less sewing.