Well, let's break it in parts, shall we?
I think that とり comes from the verb とる, which means to take.
た is the short form for たい which means "to want" and it comes in its short form when used before く in some verb conjugations. For example: 行きたい=I want to go / 行きたくない=I don't want to go.
You add く so you can add the ない which is the negation.
よ is the emphatic particle, as you said.
The whole sentence would mean: I don't want to take it or I can't take it anymore!