Can a Mole Reform After the V Beam?

It is possible that the spots were broken blood vessels that got bruised from the laser treatment.  Moles cannot re-grow from the laser.  Over time, pigmentation can recur in a mole that has been shaved flat, but that has nothing to do with the V-Beam.  If you are concerned you should return to your dermatologist and have the moles re-evaluated.

This is a temporary side effect that should resolve after 1-2 weeks.  The pigment that recurs in a mole comes up relatively gradually and is not purple but usually brown or even black. 

From the way you describe the scars left after mole removal, the moles were most likely shaved off the surface of the skin.  When moles are removed in this way, they can potentially recur from the deeper components that are usually left in the skin.  The return of the pigment is not sudden.

The purple spots represent broken blood vessels and will resolve within two week.  Moles may change colors after laser treatment, but these moles look like the typical purpura seen after V-Beam treatment.  If you still have questions after two week, check back with the doctor who did the treatment.