There is no manual saving in Dying Light. Saving occurs whenever the automatic save icon appears, as shown below. This usually takes place while crossing various checkpoints on the map, receiving quests or when leaving the game via its Pause menu:


                                             

See also:

Accidentally / Manually deleted save files

- Corrupted save files

- Steam save files location

How do I know if Steam Cloud sync works?

- [PS4] Can't play The Following anymore - it takes me back to the Slums