Can you react to the move trigger from Shadow Order Disciple with a Reaction spell?

Yes — the "When I move" trigger is a triggered ability that goes onto the chain as a Pending item, which creates a Closed State, and any player holding priority can play a Reaction spell in that window before it resolves (Rule 402.1, Rule 813.1.c.1).

Two things to keep in mind. The trigger's controller chooses whether to Burn 1 (and lose that +1 Might) at finalization, so you get your window knowing whether they're paying for it — but the burn/pump itself happens only on resolution, so killing the Disciple in response means the "give me +1 Might" instruction does nothing.

Also, the move is already complete when the trigger hits the chain — you're reacting to the pump, not to the movement, so a Reaction can't undo where the Disciple went.