You can spot mortars on the map by looking for the orange outline of a mortar and the name "weapons nest", you either get a static machine gun or a mortar. These can be found near most outposts but getting to them and using them will leave you open to a lot of enemy fire.
You can heal while operating a mortar without exiting the weapon so make sure you have some health syringes with you just in case.
I got most of my mortar kills late on in the game. During the campaign mission "A key to the North" you have to complete an objective and then you are warned that enemy reinforcements are on their way. As shown by the video below you can get loads of mortar kills defending your position during this segment.
I then went to the outpost Barnali's Textiles near this mission location and made a load of noise so that reinforcements are called (second part of video below).