There's no "quicksave" option. Instead, if you die on a mission, you will respawn a short way back from where you died. You have a limited number of these respawns per mission, and if you use them all up and then die again, you will have to restart the mission.

At first this bugged me but it was kind of nice to not have to worry about saving all the time. Also the difficulty balance was pretty well done; I usually was able to finish missions without dying, and only died a few times on the hardest missions. I don't remember which difficulty setting I was using though. Also by making you restart fully if you die too much it prevents you from getting into a situation that's too hard to win, like if all your ammo is depleted. I still would have preferred quicksaves, but the respawn system did not bother me as much as I thought it would.

Unfortunately, I don't think there's a way to continue from the middle of a mission... you can test it out by quitting the game in the middle of a mission and then going to "continue game" again and see if you start in the middle or at the beginning.

Can someone else confirm whether mid-mission restarts are possible?

Hopefully the saving system isn't too much of a detriment for you, because the game is actually quite good.