To me, it seems like it depends on the move action that you're interrupting.
If you move into the square I'm trying to enter with an interrupt, you certainly negate that action, but if I have more squares of movement left I'm fairly certain I can still use them. Perhaps the interrupt should cause me to lose one square of movement (the move that was negated), but not the whole move because, as others have pointed out, move actions resolve square by square rather than all at once.
However, since a shift is only 1 square (usually) I believe this might work differently. If I attempt to shift into square x and you interrupt that action by moving into it, I think that move action might be lost. I don't think I get to say, "Okay, I'll just shift into square y instead." Because you can clearly invalidate attacks with interrupts, I feel the precedent is clear that single square move actions should also work like this (although I'm not sure I can support that with anything explicit).
The Battlemind's Blurred Step is a much better power if this is the case. Assuming you can find a way to shift more than 1 (not the easiest thing, but possible), using Blurred Step as an opportunity action (which does interrupt) means that you can invalidate the triggering move action of the enemy (a shift). Sure he can still move away from you by spending a standard action to move, but that ain't bad. If it doesn't work like that, I remain perplexed by the purpose of the power--but that's a discussion for a different thread.