Depending on the speed at which the monopoles are emitted, they will either escape or return back to the saber’s hilt which has the opposite magnetic charge. You could of course just blast your opponent with the monopoles, but that would be rather boring. The point of a lightsaber isn’t to merely kill your enemies, but to kill them with style.
So you are emitting this stream of monopoles. Since the hilt has the opposing magnetic charge they pull after them magnetic force lines. Next you eject some electrically charged particles – electrons or ions – into this field with an initial angular velocity. These will circle in spirals around the magnetic field and, due to the circular motion, they will emit synchroton radiation, which is why you can see the blade.
Due to the emission of light and the occasional collision with air molecules, the electrically charged particles slow down and eventually escape the magnetic field. That doesn’t sound really healthy, so you might want to make sure that their kinetic energy isn’t too high. To then still get an emission spectrum with a significant contribution in the visible range, you need a huge magnetic field. Which can’t really be healthy either, but at least it decays inversely proportional to the distance from the blade.
Letting the monopoles escape has the advantage that you don’t have to devise a complicated mechanism to make sure they actually return back to the hilt. It has the disadvantage though that one fighter’s monopoles can be sucked up by the other’s saber if that has opposite charge. Can the blades pass through each other? Well, if they both have the same charges, they repel. You couldn’t easily pass them through each other, but they would probably distort each other to some extent. How much depends on the strength of the magnetic field that keeps the electrons caught.
Finally, there is the question how to produce the magnetic monopoles to begin with. For this, you need a pocket-sized accelerator that generates collision energies at the Planck scale. The most commonly used method for this is to use a Kyber crystal. This also means that you need to know string theory to accurately calculate how a lightsaber operates. May the Force be with you.
[For more speculation, see also Is a Real Lightsaber Possible? by Don Lincoln.]