With the standard open front differential, the power is going in the direction of least resistance. Since you removed the passenger side shaft there is no resistance and thus all of the "power" is being sent in that direction. Obviously there is no connection to the wheel so just the internals of the diff are spinning. There is no power going to the driver's side since it has all of the resistance.
This is why a standard open diff is considered a "1 wheel peel", or if you have one tire on ice and the other on dry pavement, only the tire on ice will spin. Same concept.