I'm trying to read manga and came across this sentence. How is "から" used here? It does definitely not mean "because", as you can see from the picture, the character is explaining his action, he does not give a reason or anything. It was translated to simply "I said no" in English. Also what does っといた mean? Is it short for っておいて or といった?
This is the 'same' から as the one you might translate "because". Here it just means something like "just so you know".
(The nuance might be slightly different, but this から could also be replaced by ので or んで, which by the way also often translates to "because".)
から (or ので or んで) is often used to convey information.
Just so you know, I [handed in my assignment / got some milk / 'll come home early today / ...]
As you suspected ～といた is a contraction of ～ておいた, see
(Just so you know,) I refused [the invitation]