It looks like it should work. It is a little more geometry specific than you are thinking, so I have modified your design below.
It will require a reasonable amount of experimentation to perfect the correct permanent magnet strength, required current, and distances to match the surface tension of mercury, etc. Other things that would need to be tested include containing the mercury droplet and bringing the droplets back together when current is reversed (if necessary).
- Green Arrows = Desired electromagnetic applied force
- Cyan Arrows = Surface tension force that must be overcome (just a generalization; it is much more complex than this)
- Yellow Arrows = Electric current (note that this is "hole current"; electrons move the opposite direction). Don't get too hung up on direction; you just reverse the polarity of the electrical current if you have it backwards.
- Purple Arrows = Magnetic field (out of and into the page respectively). Putting an iron back plate on these magnets will increase their strength. Leaving some gap between them will also increase their strength; this gap can be filled with any non-ferrous material.
- You will need to have long electrodes (as opposed to points in your drawing) so both droplets can stay in contact with the electrodes as they are pulled apart. If the current stops, so does the separating force.
- Surface tension is the force you are working against. Bringing the electrodes close together so the mercury droplet is squished will decrease the current required to separate it. If the droplet is not squished it may try to move the whole droplet one way or the other instead of separating it.
- You may need to experiment with different metals for the electrodes; some may have better "wetting" or angle of contact with the mercury droplet because of surface tension properties.
- The magnetic field through the center will not be into or out of the page, so electrical current in this area will not provide a force in the directions of concern. Possibly putting an insulator in this middle zone may improve the design.
HyperPhysics - Magnetic Force on a Current-Carrying Wire