If I had a {Desecration Demon} on the field, during the beginning of my combat step if my opponent chose to sac a creature, would I be able to {Cyclonic Rift} that creature before it gets sacrificed, leaving my demon untapped?
No. The player sacrifices as the ability's resolution, and you cannot iust cast something in the middle of something resolving. Example: you can't respond to a player's choice to take 4 damage from {Vexing Devil} to give it undying with {Undying Evil}, because the player choosing is part of the ability resolving. Same principle here.
RESOLVED