Thermoplastic
Removing Thermoplastic can be done a few ways. With enough pressure a water blaster can be used, or a sandblaster. Other ways include using a lance. The Compressed air will burn off the material. Or depending on if you have the kit available, use a scabbler. It will act as a sort of Jackhammer and break apart the material away from the road surface. In situations where the material is heavily trafficked and worn down closer to the substrate, removal is not necessary, and fresh Thermoplastic can be applied over the top. If the material still has a lot of body or a good level of thickness to it, removal is to be carried out first.
MMA/EPOXY
Strong solvents may not be useful for larger quantities of MMA that may be required for Road Markings. Some sort of abrasion or grinding equipment would be required for a material as durable as MMA/epoxy. It will wear the material down to the underlying substrate, ready for re-applying fresh product.