Weird. Maybe it didn't survive the transition from the old host site.
Well, given that "hydra heads" definitely improves their melee attacks, the waxwork unquestionably retains it, so holding the head on the stump may be foolish; you want to just wait 1d4 rounds and grow a new pair of heads.
Decapitation kills neither constructs nor hydras, so yeah, cutting off the heads won't kill them.