How did the Edo Tensei reanimated Second Mizukage summon the Giant Clam? As I understand, summoning requires blood sacrifice, contract and chakra from the jutsu user. Only Nagato (Rinnegan user) is the exception because he uses the Animal Path. He doesn't require hand seals or blood sacrifice.  

How did the Edo Tensei reanimated Second Mizukage summon the Giant Clam without blood sacrifice? I assume Edo Tensei bodies don't have blood.
He probably summoned the clam the normal way with blood. The anime / manga probably just skipped the summoning scene because this isn't a major character and the panels could be better filled with other scenes.

Edo Tensei reanimated characters do in fact have blood. I believe there are a few examples, but the only one that comes to mind at the moment is Itachi's eyes bleeding after using Amaterasu.