The Cult thinks that the pain involved in the sacrifice is cleansing for the infidel and is in fact the most important bit.
You copycat!
guillotine requires time to set up and restraining the person and has a chance of breaking with time. Far better to replicate the most efficient production line of sacrifices in history, the Aztecs
Far simpler to just push the mortal backwards over a stone and then cut out his heart with the near mechanical (and exceedingly fast) technique of the aztec priests and their sacrificial knives. Quick, simple, easy: and it is nice and personal as well.
Dual-wielding minicrossbows was my idea