し in 安心しきった寝顔

[MeitanteiJesus]

Does it function like 'and'? As in:

安心しきった寝顔
A relieved and exhausted sleeping face (きった is exhausted right?).

[Ongakuka]

きる（切る） on the end of a verb means that action is finished or complete. In this case it is on the end of the verb 安心する

[MeitanteiJesus]

Oh so し is from します and the ます is cut off for きった?

So it kind of makes 安心 into a verb?
安心 Relief
安心しきった Relieved

[Ongakuka]

Yes kiru takes the 'masu' stem of the verb. So 食べきれない = unable to finish eating （何も残さないように、最後まで食べることができない）

安心しきった寝顔 is kind of like a sleeping face that is perfectly relaxed (maybe you can think of a smoother translation)