Mersin is a coastal town in southern Turkey.
The D400 road passes through the center of the town and it is, although possibly a bit tricky, to flag down cars in the centre of Mersin. However by far the easiest way of finding a good ride from Mersin is hitchhiking anywhere on the truck-transit road which does a loop around the centre of town. A lot of trucks going far distance from one of the ports to pretty much anywhere in Turkey.
Get on the white minibusses (called Mes-koop,1.25TL) and get of at "TED Koleji", which is also end of the highway.
East to Adana, Gazi Antep, Ankara etc on the highway
There is plenty of traffic heading this direction. Your best option is to find one of the roads leading from mersin to the ring-road to the highway and hitchhike there. There are plenty of options although it may require some walking. If you're unlucky you can hitchhike on the D400 in direction Tarsus and get off at one of the onramps on the way.