You can never pay two costs with a single payment. Bloodthrone Vampire has a cost: sacrifice a creature. Eldrazi Spawn has a cost: sacrifice the Spawn. You can sacrifice it to one effect or the other, not both.
You would get one or the other. Both of them have a cost of sacrificing a creature, so you can either sac the Spawn for 1 mana, or sac it to the Vampire for +2/+2. You can't sac it for both, just like you can't buy 2 sodas from 2 different vending machines with the same dollar.
eldrazi spawn
if you sacrifice eldari spawn, would you get the 1 mana from it and still get bloodthrone vampires sacrifice effect, or just one effect?
The latest Comprehensive Rules are also good, and can be found here.