I believe the trigger is "drops 0 hitpoints", so they are doomed no matter what. I'd let the savage charge fly, it sounds very orc like and not at all out of character. Let the players take OAs, but unless they have a way to stop the movement it's going to get it's charge off. Vicious and deadly... and very scary even for a minion.
If the trigger is "drops to 0 hp" as you say, then ANY amount of damage will stop the charge. Dealing damage leads to the "resolve the effects of damage" step before the charge continues, at which point the monster will be found to have 0 hp or fewer, causing it to drop. Of course, if Savage Demise is a Trait or At-Will power it gets a new action to take before it drops, so it almost doesn't matter which interpretation is correct.