Actually one rosary consists of all 15 (now 20) mysteries. If you are praying the whole rosary, you only start the rosary once, with the Creed - Our Father - 3 Hial Marys, then you pray through all 15 or 20 mysteries. If you WANT to start over after each set of mysteries, you may, but that would only be because it is your preference, it would not be wrong.
Normally when we pray the Rosary we only pray a third of it (or a forth if your include the mysteries of Light) one set of mysteries.
If something, for eg. a requierment for a penary indulgence, states to recite a rosary, only one set of mysteries sufices to fulfil the requirements, you DO NOT need to pray the whole rosary, however you need to complete the third of the rosary in one sitting (FOR THE PENARY INDULGENCE) otherwise you receive only a partial indulgence.