Harrigan's cut goes through the middle of the gauntlet, cutting the explosive device in twain.
click to enlarge
Presumably, this disrupting the mechanism enough to prevent it from exploding. This page notes that
As the timer counts down, Harrigan manages to use the Smart Disc to sever the Predator’s arm, stopping the device from working. Interestingly, the self-destruct mechanism ceases to function however in Alien vs Predator, it is shown that it can be used as a remote explosive not connected to the Predator.
It could be that this is a plot hole, or it could be that the intent was indeed to have the self-destruct sufficiently damaged as to not function (I could see some value in not having an explosive device strapped to one's arm go off because it took a hit).
It's possible that the novelization or the shooting script contains more information, but I don't own a copy of either.