While we had our own transport while in Sri Lanka which us great flexibility to explore the region Mirissa is still easy to get to by public transport. While the train line does relatively close to Mirissa on the way to Matara, the station is inconveniently located and badly served by three wheelers so you are better off getting the bus which will drop you directly in Mirissa South. Coming from the west you can catch any bus to Matara, which pass through Mirissa. From Weligama there are regular buses costing Rs 9. From Matara you can catch buses headed west towards Weligama, Ahangama and Galle. From Matara the fare should be around Rs17. If you are heading west to Galle or Colombo, the guidebooks recommend that you head east to Matara first because it is easier to get a seat from there rather than waiting for the bus in Mirissa by which time there is a good chance the bus will be full.
If you want to go by bus or train to Colombo it´s better to go back to Matara, where bus and train are starting and you can choose your seat, in Mirissa (or Weligama for the train) the bus will be allready full.
A more fan and easier way to tour around the south coast from place to place are tuk-tuks. These are motor tricycles. You can hire one for the day and you can tour and make as much stops as you want en route. But first negotiate the price.
Keep in mind that the roads in Sri Lanka are not wide and specially in the coastal part there is heavy traffic.