Ah, so the validity period of the visa doesn't include the outbound journey? Then surely you won't be allowed to board in Stuttgart in the first place.

The fact that both arrival and departure are both from SVO/D means nothing. SVO/D is a mixed terminal with separate areas designated for international and domestic flights. One needs to undergo a passport control to get to one from another. Belarusian flights are from the domestic part, therefore you need a valid visa. :-(